1 <?xml version="1.0" encoding="utf-8"?> 2 <!DOCTYPE rfc SYSTEM 'rfc2629.dtd'> 3 <?rfc toc="yes" symrefs="yes" ?> 4 5 <rfc ipr="trust200902" category="std" docName="draft-ietf-codec-opus-14"> 6 7 <front> 8 <title abbrev="Interactive Audio Codec">Definition of the Opus Audio Codec</title> 9 10 11 <author initials="JM" surname="Valin" fullname="Jean-Marc Valin"> 12 <organization>Mozilla Corporation</organization> 13 <address> 14 <postal> 15 <street>650 Castro Street</street> 16 <city>Mountain View</city> 17 <region>CA</region> 18 <code>94041</code> 19 <country>USA</country> 20 </postal> 21 <phone>+1 650 903-0800</phone> 22 <email>jmvalin (a] jmvalin.ca</email> 23 </address> 24 </author> 25 26 <author initials="K." surname="Vos" fullname="Koen Vos"> 27 <organization>Skype Technologies S.A.</organization> 28 <address> 29 <postal> 30 <street>Soder Malarstrand 43</street> 31 <city>Stockholm</city> 32 <region></region> 33 <code>11825</code> 34 <country>SE</country> 35 </postal> 36 <phone>+46 73 085 7619</phone> 37 <email>koen.vos (a] skype.net</email> 38 </address> 39 </author> 40 41 <author initials="T." surname="Terriberry" fullname="Timothy B. Terriberry"> 42 <organization>Mozilla Corporation</organization> 43 <address> 44 <postal> 45 <street>650 Castro Street</street> 46 <city>Mountain View</city> 47 <region>CA</region> 48 <code>94041</code> 49 <country>USA</country> 50 </postal> 51 <phone>+1 650 903-0800</phone> 52 <email>tterriberry (a] mozilla.com</email> 53 </address> 54 </author> 55 56 <date day="17" month="May" year="2012" /> 57 58 <area>General</area> 59 60 <workgroup></workgroup> 61 62 <abstract> 63 <t> 64 This document defines the Opus interactive speech and audio codec. 65 Opus is designed to handle a wide range of interactive audio applications, 66 including Voice over IP, videoconferencing, in-game chat, and even live, 67 distributed music performances. 68 It scales from low bitrate narrowband speech at 6 kb/s to very high quality 69 stereo music at 510 kb/s. 70 Opus uses both linear prediction (LP) and the Modified Discrete Cosine 71 Transform (MDCT) to achieve good compression of both speech and music. 72 </t> 73 </abstract> 74 </front> 75 76 <middle> 77 78 <section anchor="introduction" title="Introduction"> 79 <t> 80 The Opus codec is a real-time interactive audio codec designed to meet the requirements 81 described in <xref target="requirements"></xref>. 82 It is composed of a linear 83 prediction (LP)-based <xref target="LPC"/> layer and a Modified Discrete Cosine Transform 84 (MDCT)-based <xref target="MDCT"/> layer. 85 The main idea behind using two layers is that in speech, linear prediction 86 techniques (such as Code-Excited Linear Prediction, or CELP) code low frequencies more efficiently than transform 87 (e.g., MDCT) domain techniques, while the situation is reversed for music and 88 higher speech frequencies. 89 Thus a codec with both layers available can operate over a wider range than 90 either one alone and, by combining them, achieve better quality than either 91 one individually. 92 </t> 93 94 <t> 95 The primary normative part of this specification is provided by the source code 96 in <xref target="ref-implementation"></xref>. 97 Only the decoder portion of this software is normative, though a 98 significant amount of code is shared by both the encoder and decoder. 99 <xref target="conformance"/> provides a decoder conformance test. 100 The decoder contains a great deal of integer and fixed-point arithmetic which 101 needs to be performed exactly, including all rounding considerations, so any 102 useful specification requires domain-specific symbolic language to adequately 103 define these operations. 104 Additionally, any 105 conflict between the symbolic representation and the included reference 106 implementation must be resolved. For the practical reasons of compatibility and 107 testability it would be advantageous to give the reference implementation 108 priority in any disagreement. The C language is also one of the most 109 widely understood human-readable symbolic representations for machine 110 behavior. 111 For these reasons this RFC uses the reference implementation as the sole 112 symbolic representation of the codec. 113 </t> 114 115 <t>While the symbolic representation is unambiguous and complete it is not 116 always the easiest way to understand the codec's operation. For this reason 117 this document also describes significant parts of the codec in English and 118 takes the opportunity to explain the rationale behind many of the more 119 surprising elements of the design. These descriptions are intended to be 120 accurate and informative, but the limitations of common English sometimes 121 result in ambiguity, so it is expected that the reader will always read 122 them alongside the symbolic representation. Numerous references to the 123 implementation are provided for this purpose. The descriptions sometimes 124 differ from the reference in ordering or through mathematical simplification 125 wherever such deviation makes an explanation easier to understand. 126 For example, the right shift and left shift operations in the reference 127 implementation are often described using division and multiplication in the text. 128 In general, the text is focused on the "what" and "why" while the symbolic 129 representation most clearly provides the "how". 130 </t> 131 132 <section anchor="notation" title="Notation and Conventions"> 133 <t> 134 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", 135 "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be 136 interpreted as described in RFC 2119 <xref target="rfc2119"></xref>. 137 </t> 138 <t> 139 Various operations in the codec require bit-exact fixed-point behavior, even 140 when writing a floating point implementation. 141 The notation "Q<n>", where n is an integer, denotes the number of binary 142 digits to the right of the decimal point in a fixed-point number. 143 For example, a signed Q14 value in a 16-bit word can represent values from 144 -2.0 to 1.99993896484375, inclusive. 145 This notation is for informational purposes only. 146 Arithmetic, when described, always operates on the underlying integer. 147 E.g., the text will explicitly indicate any shifts required after a 148 multiplication. 149 </t> 150 <t> 151 Expressions, where included in the text, follow C operator rules and 152 precedence, with the exception that the syntax "x**y" indicates x raised to 153 the power y. 154 The text also makes use of the following functions: 155 </t> 156 157 <section anchor="min" toc="exclude" title="min(x,y)"> 158 <t> 159 The smallest of two values x and y. 160 </t> 161 </section> 162 163 <section anchor="max" toc="exclude" title="max(x,y)"> 164 <t> 165 The largest of two values x and y. 166 </t> 167 </section> 168 169 <section anchor="clamp" toc="exclude" title="clamp(lo,x,hi)"> 170 <figure align="center"> 171 <artwork align="center"><![CDATA[ 172 clamp(lo,x,hi) = max(lo,min(x,hi)) 173 ]]></artwork> 174 </figure> 175 <t> 176 With this definition, if lo > hi, the lower bound is the one that 177 is enforced. 178 </t> 179 </section> 180 181 <section anchor="sign" toc="exclude" title="sign(x)"> 182 <t> 183 The sign of x, i.e., 184 <figure align="center"> 185 <artwork align="center"><![CDATA[ 186 ( -1, x < 0 , 187 sign(x) = < 0, x == 0 , 188 ( 1, x > 0 . 189 ]]></artwork> 190 </figure> 191 </t> 192 </section> 193 194 <section anchor="abs" toc="exclude" title="abs(x)"> 195 <t> 196 The absolute value of x, i.e., 197 <figure align="center"> 198 <artwork align="center"><![CDATA[ 199 abs(x) = sign(x)*x . 200 ]]></artwork> 201 </figure> 202 </t> 203 </section> 204 205 <section anchor="floor" toc="exclude" title="floor(f)"> 206 <t> 207 The largest integer z such that z <= f. 208 </t> 209 </section> 210 211 <section anchor="ceil" toc="exclude" title="ceil(f)"> 212 <t> 213 The smallest integer z such that z >= f. 214 </t> 215 </section> 216 217 <section anchor="round" toc="exclude" title="round(f)"> 218 <t> 219 The integer z nearest to f, with ties rounded towards negative infinity, 220 i.e., 221 <figure align="center"> 222 <artwork align="center"><![CDATA[ 223 round(f) = ceil(f - 0.5) . 224 ]]></artwork> 225 </figure> 226 </t> 227 </section> 228 229 <section anchor="log2" toc="exclude" title="log2(f)"> 230 <t> 231 The base-two logarithm of f. 232 </t> 233 </section> 234 235 <section anchor="ilog" toc="exclude" title="ilog(n)"> 236 <t> 237 The minimum number of bits required to store a positive integer n in two's 238 complement notation, or 0 for a non-positive integer n. 239 <figure align="center"> 240 <artwork align="center"><![CDATA[ 241 ( 0, n <= 0, 242 ilog(n) = < 243 ( floor(log2(n))+1, n > 0 244 ]]></artwork> 245 </figure> 246 Examples: 247 <list style="symbols"> 248 <t>ilog(-1) = 0</t> 249 <t>ilog(0) = 0</t> 250 <t>ilog(1) = 1</t> 251 <t>ilog(2) = 2</t> 252 <t>ilog(3) = 2</t> 253 <t>ilog(4) = 3</t> 254 <t>ilog(7) = 3</t> 255 </list> 256 </t> 257 </section> 258 259 </section> 260 261 </section> 262 263 <section anchor="overview" title="Opus Codec Overview"> 264 265 <t> 266 The Opus codec scales from 6 kb/s narrowband mono speech to 510 kb/s 267 fullband stereo music, with algorithmic delays ranging from 5 ms to 268 65.2 ms. 269 At any given time, either the LP layer, the MDCT layer, or both, may be active. 270 It can seamlessly switch between all of its various operating modes, giving it 271 a great deal of flexibility to adapt to varying content and network 272 conditions without renegotiating the current session. 273 The codec allows input and output of various audio bandwidths, defined as 274 follows: 275 </t> 276 <texttable anchor="audio-bandwidth"> 277 <ttcol>Abbreviation</ttcol> 278 <ttcol align="right">Audio Bandwidth</ttcol> 279 <ttcol align="right">Sample Rate (Effective)</ttcol> 280 <c>NB (narrowband)</c> <c>4 kHz</c> <c>8 kHz</c> 281 <c>MB (medium-band)</c> <c>6 kHz</c> <c>12 kHz</c> 282 <c>WB (wideband)</c> <c>8 kHz</c> <c>16 kHz</c> 283 <c>SWB (super-wideband)</c> <c>12 kHz</c> <c>24 kHz</c> 284 <c>FB (fullband)</c> <c>20 kHz (*)</c> <c>48 kHz</c> 285 </texttable> 286 <t> 287 (*) Although the sampling theorem allows a bandwidth as large as half the 288 sampling rate, Opus never codes audio above 20 kHz, as that is the 289 generally accepted upper limit of human hearing. 290 </t> 291 292 <t> 293 Opus defines super-wideband (SWB) with an effective sample rate of 24 kHz, 294 unlike some other audio coding standards that use 32 kHz. 295 This was chosen for a number of reasons. 296 The band layout in the MDCT layer naturally allows skipping coefficients for 297 frequencies over 12 kHz, but does not allow cleanly dropping just those 298 frequencies over 16 kHz. 299 A sample rate of 24 kHz also makes resampling in the MDCT layer easier, 300 as 24 evenly divides 48, and when 24 kHz is sufficient, it can save 301 computation in other processing, such as Acoustic Echo Cancellation (AEC). 302 Experimental changes to the band layout to allow a 16 kHz cutoff 303 (32 kHz effective sample rate) showed potential quality degradations at 304 other sample rates, and at typical bitrates the number of bits saved by using 305 such a cutoff instead of coding in fullband (FB) mode is very small. 306 Therefore, if an application wishes to process a signal sampled at 32 kHz, 307 it should just use FB. 308 </t> 309 310 <t> 311 The LP layer is based on the SILK codec 312 <xref target="SILK"></xref>. 313 It supports NB, MB, or WB audio and frame sizes from 10 ms to 60 ms, 314 and requires an additional 5 ms look-ahead for noise shaping estimation. 315 A small additional delay (up to 1.5 ms) may be required for sampling rate 316 conversion. 317 Like Vorbis <xref target='Vorbis-website'/> and many other modern codecs, SILK is inherently designed for 318 variable-bitrate (VBR) coding, though the encoder can also produce 319 constant-bitrate (CBR) streams. 320 The version of SILK used in Opus is substantially modified from, and not 321 compatible with, the stand-alone SILK codec previously deployed by Skype. 322 This document does not serve to define that format, but those interested in the 323 original SILK codec should see <xref target="SILK"/> instead. 324 </t> 325 326 <t> 327 The MDCT layer is based on the CELT codec <xref target="CELT"></xref>. 328 It supports NB, WB, SWB, or FB audio and frame sizes from 2.5 ms to 329 20 ms, and requires an additional 2.5 ms look-ahead due to the 330 overlapping MDCT windows. 331 The CELT codec is inherently designed for CBR coding, but unlike many CBR 332 codecs it is not limited to a set of predetermined rates. 333 It internally allocates bits to exactly fill any given target budget, and an 334 encoder can produce a VBR stream by varying the target on a per-frame basis. 335 The MDCT layer is not used for speech when the audio bandwidth is WB or less, 336 as it is not useful there. 337 On the other hand, non-speech signals are not always adequately coded using 338 linear prediction, so for music only the MDCT layer should be used. 339 </t> 340 341 <t> 342 A "Hybrid" mode allows the use of both layers simultaneously with a frame size 343 of 10 or 20 ms and a SWB or FB audio bandwidth. 344 The LP layer codes the low frequencies by resampling the signal down to WB. 345 The MDCT layer follows, coding the high frequency portion of the signal. 346 The cutoff between the two lies at 8 kHz, the maximum WB audio bandwidth. 347 In the MDCT layer, all bands below 8 kHz are discarded, so there is no 348 coding redundancy between the two layers. 349 </t> 350 351 <t> 352 The sample rate (in contrast to the actual audio bandwidth) can be chosen 353 independently on the encoder and decoder side, e.g., a fullband signal can be 354 decoded as wideband, or vice versa. 355 This approach ensures a sender and receiver can always interoperate, regardless 356 of the capabilities of their actual audio hardware. 357 Internally, the LP layer always operates at a sample rate of twice the audio 358 bandwidth, up to a maximum of 16 kHz, which it continues to use for SWB 359 and FB. 360 The decoder simply resamples its output to support different sample rates. 361 The MDCT layer always operates internally at a sample rate of 48 kHz. 362 Since all the supported sample rates evenly divide this rate, and since the 363 the decoder may easily zero out the high frequency portion of the spectrum in 364 the frequency domain, it can simply decimate the MDCT layer output to achieve 365 the other supported sample rates very cheaply. 366 </t> 367 368 <t> 369 After conversion to the common, desired output sample rate, the decoder simply 370 adds the output from the two layers together. 371 To compensate for the different look-ahead required by each layer, the CELT 372 encoder input is delayed by an additional 2.7 ms. 373 This ensures that low frequencies and high frequencies arrive at the same time. 374 This extra delay may be reduced by an encoder by using less look-ahead for noise 375 shaping or using a simpler resampler in the LP layer, but this will reduce 376 quality. 377 However, the base 2.5 ms look-ahead in the CELT layer cannot be reduced in 378 the encoder because it is needed for the MDCT overlap, whose size is fixed by 379 the decoder. 380 </t> 381 382 <t> 383 Both layers use the same entropy coder, avoiding any waste from "padding bits" 384 between them. 385 The hybrid approach makes it easy to support both CBR and VBR coding. 386 Although the LP layer is VBR, the bit allocation of the MDCT layer can produce 387 a final stream that is CBR by using all the bits left unused by the LP layer. 388 </t> 389 390 <section title="Control Parameters"> 391 <t> 392 The Opus codec includes a number of control parameters which can be changed dynamically during 393 regular operation of the codec, without interrupting the audio stream from the encoder to the decoder. 394 These parameters only affect the encoder since any impact they have on the bit-stream is signaled 395 in-band such that a decoder can decode any Opus stream without any out-of-band signaling. Any Opus 396 implementation can add or modify these control parameters without affecting interoperability. The most 397 important encoder control parameters in the reference encoder are listed below. 398 </t> 399 400 <section title="Bitrate" toc="exlcude"> 401 <t> 402 Opus supports all bitrates from 6 kb/s to 510 kb/s. All other parameters being 403 equal, higher bitrate results in higher quality. For a frame size of 20 ms, these 404 are the bitrate "sweet spots" for Opus in various configurations: 405 <list style="symbols"> 406 <t>8-12 kb/s for NB speech,</t> 407 <t>16-20 kb/s for WB speech,</t> 408 <t>28-40 kb/s for FB speech,</t> 409 <t>48-64 kb/s for FB mono music, and</t> 410 <t>64-128 kb/s for FB stereo music.</t> 411 </list> 412 </t> 413 </section> 414 415 <section title="Number of Channels (Mono/Stereo)" toc="exlcude"> 416 <t> 417 Opus can transmit either mono or stereo frames within a single stream. 418 When decoding a mono frame in a stereo decoder, the left and right channels are 419 identical, and when decoding a stereo frame in a mono decoder, the mono output 420 is the average of the left and right channels. 421 In some cases, it is desirable to encode a stereo input stream in mono (e.g., 422 because the bitrate is too low to encode stereo with sufficient quality). 423 The number of channels encoded can be selected in real-time, but by default the 424 reference encoder attempts to make the best decision possible given the 425 current bitrate. 426 </t> 427 </section> 428 429 <section title="Audio Bandwidth" toc="exlcude"> 430 <t> 431 The audio bandwidths supported by Opus are listed in 432 <xref target="audio-bandwidth"/>. 433 Just like for the number of channels, any decoder can decode audio encoded at 434 any bandwidth. 435 For example, any Opus decoder operating at 8 kHz can decode a FB Opus 436 frame, and any Opus decoder operating at 48 kHz can decode a NB frame. 437 Similarly, the reference encoder can take a 48 kHz input signal and 438 encode it as NB. 439 The higher the audio bandwidth, the higher the required bitrate to achieve 440 acceptable quality. 441 The audio bandwidth can be explicitly specified in real-time, but by default 442 the reference encoder attempts to make the best bandwidth decision possible 443 given the current bitrate. 444 </t> 445 </section> 446 447 448 <section title="Frame Duration" toc="exlcude"> 449 <t> 450 Opus can encode frames of 2.5, 5, 10, 20, 40 or 60 ms. 451 It can also combine multiple frames into packets of up to 120 ms. 452 For real-time applications, sending fewer packets per second reduces the 453 bitrate, since it reduces the overhead from IP, UDP, and RTP headers. 454 However, it increases latency and sensitivity to packet losses, as losing one 455 packet constitutes a loss of a bigger chunk of audio. 456 Increasing the frame duration also slightly improves coding efficiency, but the 457 gain becomes small for frame sizes above 20 ms. 458 For this reason, 20 ms frames are a good choice for most applications. 459 </t> 460 </section> 461 462 <section title="Complexity" toc="exlcude"> 463 <t> 464 There are various aspects of the Opus encoding process where trade-offs 465 can be made between CPU complexity and quality/bitrate. In the reference 466 encoder, the complexity is selected using an integer from 0 to 10, where 467 0 is the lowest complexity and 10 is the highest. Examples of 468 computations for which such trade-offs may occur are: 469 <list style="symbols"> 470 <t>The order of the pitch analysis whitening filter <xref target="Whitening"/>,</t> 471 <t>The order of the short-term noise shaping filter,</t> 472 <t>The number of states in delayed decision quantization of the 473 residual signal, and</t> 474 <t>The use of certain bit-stream features such as variable time-frequency 475 resolution and the pitch post-filter.</t> 476 </list> 477 </t> 478 </section> 479 480 <section title="Packet Loss Resilience" toc="exlcude"> 481 <t> 482 Audio codecs often exploit inter-frame correlations to reduce the 483 bitrate at a cost in error propagation: after losing one packet 484 several packets need to be received before the decoder is able to 485 accurately reconstruct the speech signal. The extent to which Opus 486 exploits inter-frame dependencies can be adjusted on the fly to 487 choose a trade-off between bitrate and amount of error propagation. 488 </t> 489 </section> 490 491 <section title="Forward Error Correction (FEC)" toc="exlcude"> 492 <t> 493 Another mechanism providing robustness against packet loss is the in-band 494 Forward Error Correction (FEC). Packets that are determined to 495 contain perceptually important speech information, such as onsets or 496 transients, are encoded again at a lower bitrate and this re-encoded 497 information is added to a subsequent packet. 498 </t> 499 </section> 500 501 <section title="Constant/Variable Bitrate" toc="exlcude"> 502 <t> 503 Opus is more efficient when operating with variable bitrate (VBR), which is 504 the default. However, in some (rare) applications, constant bitrate (CBR) 505 is required. There are two main reasons to operate in CBR mode: 506 <list style="symbols"> 507 <t>When the transport only supports a fixed size for each compressed frame</t> 508 <t>When encryption is used for an audio stream that is either highly constrained 509 (e.g. yes/no, recorded prompts) or highly sensitive <xref target="SRTP-VBR"></xref> </t> 510 </list> 511 512 When low-latency transmission is required over a relatively slow connection, then 513 constrained VBR can also be used. This uses VBR in a way that simulates a 514 "bit reservoir" and is equivalent to what MP3 (MPEG 1, Layer 3) and 515 AAC (Advanced Audio Coding) call CBR (i.e., not true 516 CBR due to the bit reservoir). 517 </t> 518 </section> 519 520 <section title="Discontinuous Transmission (DTX)" toc="exlcude"> 521 <t> 522 Discontinuous Transmission (DTX) reduces the bitrate during silence 523 or background noise. When DTX is enabled, only one frame is encoded 524 every 400 milliseconds. 525 </t> 526 </section> 527 528 </section> 529 530 </section> 531 532 <section anchor="modes" title="Internal Framing"> 533 534 <t> 535 The Opus encoder produces "packets", which are each a contiguous set of bytes 536 meant to be transmitted as a single unit. 537 The packets described here do not include such things as IP, UDP, or RTP 538 headers which are normally found in a transport-layer packet. 539 A single packet may contain multiple audio frames, so long as they share a 540 common set of parameters, including the operating mode, audio bandwidth, frame 541 size, and channel count (mono vs. stereo). 542 This section describes the possible combinations of these parameters and the 543 internal framing used to pack multiple frames into a single packet. 544 This framing is not self-delimiting. 545 Instead, it assumes that a higher layer (such as UDP or RTP <xref target='RFC3550'/> 546 or Ogg <xref target='RFC3533'/> or Matroska <xref target='Matroska-website'/>) 547 will communicate the length, in bytes, of the packet, and it uses this 548 information to reduce the framing overhead in the packet itself. 549 A decoder implementation MUST support the framing described in this section. 550 An alternative, self-delimiting variant of the framing is described in 551 <xref target="self-delimiting-framing"/>. 552 Support for that variant is OPTIONAL. 553 </t> 554 555 <t> 556 All bit diagrams in this document number the bits so that bit 0 is the most 557 significant bit of the first byte, and bit 7 is the least significant. 558 Bit 8 is thus the most significant bit of the second byte, etc. 559 Well-formed Opus packets obey certain requirements, marked [R1] through [R7] 560 below. 561 These are summarized in <xref target="malformed-packets"/> along with 562 appropriate means of handling malformed packets. 563 </t> 564 565 <section anchor="toc_byte" title="The TOC Byte"> 566 <t anchor="R1"> 567 A well-formed Opus packet MUST contain at least one byte [R1]. 568 This byte forms a table-of-contents (TOC) header that signals which of the 569 various modes and configurations a given packet uses. 570 It is composed of a configuration number, "config", a stereo flag, "s", and a 571 frame count code, "c", arranged as illustrated in 572 <xref target="toc_byte_fig"/>. 573 A description of each of these fields follows. 574 </t> 575 576 <figure anchor="toc_byte_fig" title="The TOC Byte"> 577 <artwork align="center"><![CDATA[ 578 0 579 0 1 2 3 4 5 6 7 580 +-+-+-+-+-+-+-+-+ 581 | config |s| c | 582 +-+-+-+-+-+-+-+-+ 583 ]]></artwork> 584 </figure> 585 586 <t> 587 The top five bits of the TOC byte, labeled "config", encode one of 32 possible 588 configurations of operating mode, audio bandwidth, and frame size. 589 As described, the LP (SILK) layer and MDCT (CELT) layer can be combined in three possible 590 operating modes: 591 <list style="numbers"> 592 <t>A SILK-only mode for use in low bitrate connections with an audio bandwidth 593 of WB or less,</t> 594 <t>A Hybrid (SILK+CELT) mode for SWB or FB speech at medium bitrates, and</t> 595 <t>A CELT-only mode for very low delay speech transmission as well as music 596 transmission (NB to FB).</t> 597 </list> 598 The 32 possible configurations each identify which one of these operating modes 599 the packet uses, as well as the audio bandwidth and the frame size. 600 <xref target="config_bits"/> lists the parameters for each configuration. 601 </t> 602 <texttable anchor="config_bits" title="TOC Byte Configuration Parameters"> 603 <ttcol>Configuration Number(s)</ttcol> 604 <ttcol>Mode</ttcol> 605 <ttcol>Bandwidth</ttcol> 606 <ttcol>Frame Sizes</ttcol> 607 <c>0...3</c> <c>SILK-only</c> <c>NB</c> <c>10, 20, 40, 60 ms</c> 608 <c>4...7</c> <c>SILK-only</c> <c>MB</c> <c>10, 20, 40, 60 ms</c> 609 <c>8...11</c> <c>SILK-only</c> <c>WB</c> <c>10, 20, 40, 60 ms</c> 610 <c>12...13</c> <c>Hybrid</c> <c>SWB</c> <c>10, 20 ms</c> 611 <c>14...15</c> <c>Hybrid</c> <c>FB</c> <c>10, 20 ms</c> 612 <c>16...19</c> <c>CELT-only</c> <c>NB</c> <c>2.5, 5, 10, 20 ms</c> 613 <c>20...23</c> <c>CELT-only</c> <c>WB</c> <c>2.5, 5, 10, 20 ms</c> 614 <c>24...27</c> <c>CELT-only</c> <c>SWB</c> <c>2.5, 5, 10, 20 ms</c> 615 <c>28...31</c> <c>CELT-only</c> <c>FB</c> <c>2.5, 5, 10, 20 ms</c> 616 </texttable> 617 <t> 618 The configuration numbers in each range (e.g., 0...3 for NB SILK-only) 619 correspond to the various choices of frame size, in the same order. 620 For example, configuration 0 has a 10 ms frame size and configuration 3 621 has a 60 ms frame size. 622 </t> 623 624 <t> 625 One additional bit, labeled "s", signals mono vs. stereo, with 0 indicating 626 mono and 1 indicating stereo. 627 </t> 628 629 <t> 630 The remaining two bits of the TOC byte, labeled "c", code the number of frames 631 per packet (codes 0 to 3) as follows: 632 <list style="symbols"> 633 <t>0: 1 frame in the packet</t> 634 <t>1: 2 frames in the packet, each with equal compressed size</t> 635 <t>2: 2 frames in the packet, with different compressed sizes</t> 636 <t>3: an arbitrary number of frames in the packet</t> 637 </list> 638 This draft refers to a packet as a code 0 packet, code 1 packet, etc., based on 639 the value of "c". 640 </t> 641 642 </section> 643 644 <section title="Frame Packing"> 645 646 <t> 647 This section describes how frames are packed according to each possible value 648 of "c" in the TOC byte. 649 </t> 650 651 <section anchor="frame-length-coding" title="Frame Length Coding"> 652 <t> 653 When a packet contains multiple VBR frames (i.e., code 2 or 3), the compressed 654 length of one or more of these frames is indicated with a one- or two-byte 655 sequence, with the meaning of the first byte as follows: 656 <list style="symbols"> 657 <t>0: No frame (discontinuous transmission (DTX) or lost packet)</t> 658 <t>1...251: Length of the frame in bytes</t> 659 <t>252...255: A second byte is needed. The total length is (second_byte*4)+first_byte</t> 660 </list> 661 </t> 662 663 <t> 664 The special length 0 indicates that no frame is available, either because it 665 was dropped during transmission by some intermediary or because the encoder 666 chose not to transmit it. 667 Any Opus frame in any mode MAY have a length of 0. 668 </t> 669 670 <t> 671 The maximum representable length is 255*4+255=1275 bytes. 672 For 20 ms frames, this represents a bitrate of 510 kb/s, which is 673 approximately the highest useful rate for lossily compressed fullband stereo 674 music. 675 Beyond this point, lossless codecs are more appropriate. 676 It is also roughly the maximum useful rate of the MDCT layer, as shortly 677 thereafter quality no longer improves with additional bits due to limitations 678 on the codebook sizes. 679 </t> 680 681 <t anchor="R2"> 682 No length is transmitted for the last frame in a VBR packet, or for any of the 683 frames in a CBR packet, as it can be inferred from the total size of the 684 packet and the size of all other data in the packet. 685 However, the length of any individual frame MUST NOT exceed 686 1275 bytes [R2], to allow for repacketization by gateways, 687 conference bridges, or other software. 688 </t> 689 </section> 690 691 <section title="Code 0: One Frame in the Packet"> 692 693 <t> 694 For code 0 packets, the TOC byte is immediately followed by N-1 bytes 695 of compressed data for a single frame (where N is the size of the packet), 696 as illustrated in <xref target="code0_packet"/>. 697 </t> 698 <figure anchor="code0_packet" title="A Code 0 Packet" align="center"> 699 <artwork align="center"><![CDATA[ 700 0 1 2 3 701 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 702 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 703 | config |s|0|0| | 704 +-+-+-+-+-+-+-+-+ | 705 | Compressed frame 1 (N-1 bytes)... : 706 : | 707 | | 708 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 709 ]]></artwork> 710 </figure> 711 </section> 712 713 <section title="Code 1: Two Frames in the Packet, Each with Equal Compressed Size"> 714 <t anchor="R3"> 715 For code 1 packets, the TOC byte is immediately followed by the 716 (N-1)/2 bytes of compressed data for the first frame, followed by 717 (N-1)/2 bytes of compressed data for the second frame, as illustrated in 718 <xref target="code1_packet"/>. 719 The number of payload bytes available for compressed data, N-1, MUST be even 720 for all code 1 packets [R3]. 721 </t> 722 <figure anchor="code1_packet" title="A Code 1 Packet" align="center"> 723 <artwork align="center"><![CDATA[ 724 0 1 2 3 725 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 726 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 727 | config |s|0|1| | 728 +-+-+-+-+-+-+-+-+ : 729 | Compressed frame 1 ((N-1)/2 bytes)... | 730 : +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 731 | | | 732 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ : 733 | Compressed frame 2 ((N-1)/2 bytes)... | 734 : +-+-+-+-+-+-+-+-+ 735 | | 736 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 737 ]]></artwork> 738 </figure> 739 </section> 740 741 <section title="Code 2: Two Frames in the Packet, with Different Compressed Sizes"> 742 <t anchor="R4"> 743 For code 2 packets, the TOC byte is followed by a one- or two-byte sequence 744 indicating the length of the first frame (marked N1 in <xref target='code2_packet'/>), 745 followed by N1 bytes of compressed data for the first frame. 746 The remaining N-N1-2 or N-N1-3 bytes are the compressed data for the 747 second frame. 748 This is illustrated in <xref target="code2_packet"/>. 749 A code 2 packet MUST contain enough bytes to represent a valid length. 750 For example, a 1-byte code 2 packet is always invalid, and a 2-byte code 2 751 packet whose second byte is in the range 252...255 is also invalid. 752 The length of the first frame, N1, MUST also be no larger than the size of the 753 payload remaining after decoding that length for all code 2 packets [R4]. 754 This makes, for example, a 2-byte code 2 packet with a second byte in the range 755 1...251 invalid as well (the only valid 2-byte code 2 packet is one where the 756 length of both frames is zero). 757 </t> 758 <figure anchor="code2_packet" title="A Code 2 Packet" align="center"> 759 <artwork align="center"><![CDATA[ 760 0 1 2 3 761 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 762 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 763 | config |s|1|0| N1 (1-2 bytes): | 764 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ : 765 | Compressed frame 1 (N1 bytes)... | 766 : +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 767 | | | 768 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | 769 | Compressed frame 2... : 770 : | 771 | | 772 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 773 ]]></artwork> 774 </figure> 775 </section> 776 777 <section title="Code 3: A Signaled Number of Frames in the Packet"> 778 <t anchor="R5"> 779 Code 3 packets signal the number of frames, as well as additional 780 padding, called "Opus padding" to indicate that this padding is added at the 781 Opus layer, rather than at the transport layer. 782 Code 3 packets MUST have at least 2 bytes [R6,R7]. 783 The TOC byte is followed by a byte encoding the number of frames in the packet 784 in bits 2 to 7 (marked "M" in <xref target='frame_count_byte'/>), with bit 1 indicating whether 785 or not Opus padding is inserted (marked "p" in <xref target='frame_count_byte'/>), and bit 0 786 indicating VBR (marked "v" in <xref target='frame_count_byte'/>). 787 M MUST NOT be zero, and the audio duration contained within a packet MUST NOT 788 exceed 120 ms [R5]. 789 This limits the maximum frame count for any frame size to 48 (for 2.5 ms 790 frames), with lower limits for longer frame sizes. 791 <xref target="frame_count_byte"/> illustrates the layout of the frame count 792 byte. 793 </t> 794 <figure anchor="frame_count_byte" title="The frame count byte"> 795 <artwork align="center"><![CDATA[ 796 0 797 0 1 2 3 4 5 6 7 798 +-+-+-+-+-+-+-+-+ 799 |v|p| M | 800 +-+-+-+-+-+-+-+-+ 801 ]]></artwork> 802 </figure> 803 <t> 804 When Opus padding is used, the number of bytes of padding is encoded in the 805 bytes following the frame count byte. 806 Values from 0...254 indicate that 0...254 bytes of padding are included, 807 in addition to the byte(s) used to indicate the size of the padding. 808 If the value is 255, then the size of the additional padding is 254 bytes, 809 plus the padding value encoded in the next byte. 810 There MUST be at least one more byte in the packet in this case [R6,R7]. 811 The additional padding bytes appear at the end of the packet, and MUST be set 812 to zero by the encoder to avoid creating a covert channel. 813 The decoder MUST accept any value for the padding bytes, however. 814 </t> 815 <t> 816 Although this encoding provides multiple ways to indicate a given number of 817 padding bytes, each uses a different number of bytes to indicate the padding 818 size, and thus will increase the total packet size by a different amount. 819 For example, to add 255 bytes to a packet, set the padding bit, p, to 1, insert 820 a single byte after the frame count byte with a value of 254, and append 254 821 padding bytes with the value zero to the end of the packet. 822 To add 256 bytes to a packet, set the padding bit to 1, insert two bytes after 823 the frame count byte with the values 255 and 0, respectively, and append 254 824 padding bytes with the value zero to the end of the packet. 825 By using the value 255 multiple times, it is possible to create a packet of any 826 specific, desired size. 827 Let P be the number of header bytes used to indicate the padding size plus the 828 number of padding bytes themselves (i.e., P is the total number of bytes added 829 to the packet). 830 Then P MUST be no more than N-2 [R6,R7]. 831 </t> 832 <t anchor="R6"> 833 In the CBR case, let R=N-2-P be the number of bytes remaining in the packet 834 after subtracting the (optional) padding. 835 Then the compressed length of each frame in bytes is equal to R/M. 836 The value R MUST be a non-negative integer multiple of M [R6]. 837 The compressed data for all M frames follows, each of size 838 R/M bytes, as illustrated in <xref target="code3cbr_packet"/>. 839 </t> 840 841 <figure anchor="code3cbr_packet" title="A CBR Code 3 Packet" align="center"> 842 <artwork align="center"><![CDATA[ 843 0 1 2 3 844 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 845 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 846 | config |s|1|1|0|p| M | Padding length (Optional) : 847 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 848 | | 849 : Compressed frame 1 (R/M bytes)... : 850 | | 851 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 852 | | 853 : Compressed frame 2 (R/M bytes)... : 854 | | 855 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 856 | | 857 : ... : 858 | | 859 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 860 | | 861 : Compressed frame M (R/M bytes)... : 862 | | 863 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 864 : Opus Padding (Optional)... | 865 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 866 ]]></artwork> 867 </figure> 868 869 <t anchor="R7"> 870 In the VBR case, the (optional) padding length is followed by M-1 frame 871 lengths (indicated by "N1" to "N[M-1]" in <xref target='code3vbr_packet'/>), each encoded in a 872 one- or two-byte sequence as described above. 873 The packet MUST contain enough data for the M-1 lengths after removing the 874 (optional) padding, and the sum of these lengths MUST be no larger than the 875 number of bytes remaining in the packet after decoding them [R7]. 876 The compressed data for all M frames follows, each frame consisting of the 877 indicated number of bytes, with the final frame consuming any remaining bytes 878 before the final padding, as illustrated in <xref target="code3cbr_packet"/>. 879 The number of header bytes (TOC byte, frame count byte, padding length bytes, 880 and frame length bytes), plus the signaled length of the first M-1 frames themselves, 881 plus the signaled length of the padding MUST be no larger than N, the total size of the 882 packet. 883 </t> 884 885 <figure anchor="code3vbr_packet" title="A VBR Code 3 Packet" align="center"> 886 <artwork align="center"><![CDATA[ 887 0 1 2 3 888 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 889 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 890 | config |s|1|1|1|p| M | Padding length (Optional) : 891 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 892 : N1 (1-2 bytes): N2 (1-2 bytes): ... : N[M-1] | 893 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 894 | | 895 : Compressed frame 1 (N1 bytes)... : 896 | | 897 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 898 | | 899 : Compressed frame 2 (N2 bytes)... : 900 | | 901 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 902 | | 903 : ... : 904 | | 905 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 906 | | 907 : Compressed frame M... : 908 | | 909 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 910 : Opus Padding (Optional)... | 911 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 912 ]]></artwork> 913 </figure> 914 </section> 915 </section> 916 917 <section anchor="examples" title="Examples"> 918 <t> 919 Simplest case, one NB mono 20 ms SILK frame: 920 </t> 921 922 <figure anchor='framing_example_1'> 923 <artwork><![CDATA[ 924 0 1 2 3 925 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 926 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 927 | 1 |0|0|0| compressed data... : 928 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 929 ]]></artwork> 930 </figure> 931 932 <t> 933 Two FB mono 5 ms CELT frames of the same compressed size: 934 </t> 935 936 <figure anchor='framing_example_2'> 937 <artwork><![CDATA[ 938 0 1 2 3 939 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 940 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 941 | 29 |0|0|1| compressed data... : 942 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 943 ]]></artwork> 944 </figure> 945 946 <t> 947 Two FB mono 20 ms Hybrid frames of different compressed size: 948 </t> 949 950 <figure anchor='framing_example_3'> 951 <artwork><![CDATA[ 952 0 1 2 3 953 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 954 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 955 | 15 |0|1|1|1|0| 2 | N1 | | 956 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | 957 | compressed data... : 958 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 959 ]]></artwork> 960 </figure> 961 962 <t> 963 Four FB stereo 20 ms CELT frames of the same compressed size: 964 </t> 965 966 <figure anchor='framing_example_4'> 967 <artwork><![CDATA[ 968 0 1 2 3 969 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 970 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 971 | 31 |1|1|1|0|0| 4 | compressed data... : 972 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 973 ]]></artwork> 974 </figure> 975 </section> 976 977 <section anchor="malformed-packets" title="Receiving Malformed Packets"> 978 <t> 979 A receiver MUST NOT process packets which violate any of the rules above as 980 normal Opus packets. 981 They are reserved for future applications, such as in-band headers (containing 982 metadata, etc.). 983 Packets which violate these constraints may cause implementations of 984 <spanx style="emph">this</spanx> specification to treat them as malformed, and 985 discard them. 986 </t> 987 <t> 988 These constraints are summarized here for reference: 989 <list style="format [R%d]"> 990 <t>Packets are at least one byte.</t> 991 <t>No implicit frame length is larger than 1275 bytes.</t> 992 <t>Code 1 packets have an odd total length, N, so that (N-1)/2 is an 993 integer.</t> 994 <t>Code 2 packets have enough bytes after the TOC for a valid frame 995 length, and that length is no larger than the number of bytes remaining in the 996 packet.</t> 997 <t>Code 3 packets contain at least one frame, but no more than 120 ms 998 of audio total.</t> 999 <t>The length of a CBR code 3 packet, N, is at least two bytes, the number of 1000 bytes added to indicate the padding size plus the trailing padding bytes 1001 themselves, P, is no more than N-2, and the frame count, M, satisfies 1002 the constraint that (N-2-P) is a non-negative integer multiple of M.</t> 1003 <t>VBR code 3 packets are large enough to contain all the header bytes (TOC 1004 byte, frame count byte, any padding length bytes, and any frame length bytes), 1005 plus the length of the first M-1 frames, plus any trailing padding bytes.</t> 1006 </list> 1007 </t> 1008 </section> 1009 1010 </section> 1011 1012 <section title="Opus Decoder"> 1013 <t> 1014 The Opus decoder consists of two main blocks: the SILK decoder and the CELT 1015 decoder. 1016 At any given time, one or both of the SILK and CELT decoders may be active. 1017 The output of the Opus decode is the sum of the outputs from the SILK and CELT 1018 decoders with proper sample rate conversion and delay compensation on the SILK 1019 side, and optional decimation (when decoding to sample rates less than 1020 48 kHz) on the CELT side, as illustrated in the block diagram below. 1021 </t> 1022 <figure> 1023 <artwork> 1024 <![CDATA[ 1025 +---------+ +------------+ 1026 | SILK | | Sample | 1027 +->| Decoder |--->| Rate |----+ 1028 Bit- +---------+ | | | | Conversion | v 1029 stream | Range |---+ +---------+ +------------+ /---\ Audio 1030 ------->| Decoder | | + |------> 1031 | |---+ +---------+ +------------+ \---/ 1032 +---------+ | | CELT | | Decimation | ^ 1033 +->| Decoder |--->| (Optional) |----+ 1034 | | | | 1035 +---------+ +------------+ 1036 ]]> 1037 </artwork> 1038 </figure> 1039 1040 <section anchor="range-decoder" title="Range Decoder"> 1041 <t> 1042 Opus uses an entropy coder based on range coding <xref target="range-coding"></xref> 1043 <xref target="Martin79"></xref>, 1044 which is itself a rediscovery of the FIFO arithmetic code introduced by <xref target="coding-thesis"></xref>. 1045 It is very similar to arithmetic encoding, except that encoding is done with 1046 digits in any base instead of with bits, 1047 so it is faster when using larger bases (i.e., a byte). All of the 1048 calculations in the range coder must use bit-exact integer arithmetic. 1049 </t> 1050 <t> 1051 Symbols may also be coded as "raw bits" packed directly into the bitstream, 1052 bypassing the range coder. 1053 These are packed backwards starting at the end of the frame, as illustrated in 1054 <xref target="rawbits-example"/>. 1055 This reduces complexity and makes the stream more resilient to bit errors, as 1056 corruption in the raw bits will not desynchronize the decoding process, unlike 1057 corruption in the input to the range decoder. 1058 Raw bits are only used in the CELT layer. 1059 </t> 1060 1061 <figure anchor="rawbits-example" title="Illustrative example of packing range 1062 coder and raw bits data"> 1063 <artwork align="center"><![CDATA[ 1064 0 1 2 3 1065 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 1066 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 1067 | Range coder data (packed MSB to LSB) -> : 1068 + + 1069 : : 1070 + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 1071 : | <- Boundary occurs at an arbitrary bit position : 1072 +-+-+-+ + 1073 : <- Raw bits data (packed LSB to MSB) | 1074 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 1075 ]]></artwork> 1076 </figure> 1077 1078 <t> 1079 Each symbol coded by the range coder is drawn from a finite alphabet and coded 1080 in a separate "context", which describes the size of the alphabet and the 1081 relative frequency of each symbol in that alphabet. 1082 </t> 1083 <t> 1084 Suppose there is a context with n symbols, identified with an index that ranges 1085 from 0 to n-1. 1086 The parameters needed to encode or decode symbol k in this context are 1087 represented by a three-tuple (fl[k], fh[k], ft), with 1088 0 <= fl[k] < fh[k] <= ft <= 65535. 1089 The values of this tuple are derived from the probability model for the 1090 symbol, represented by traditional "frequency counts". 1091 Because Opus uses static contexts these are not updated as symbols are decoded. 1092 Let f[i] be the frequency of symbol i. 1093 Then the three-tuple corresponding to symbol k is given by 1094 </t> 1095 <figure align="center"> 1096 <artwork align="center"><![CDATA[ 1097 k-1 n-1 1098 __ __ 1099 fl[k] = \ f[i], fh[k] = fl[k] + f[k], ft = \ f[i] 1100 /_ /_ 1101 i=0 i=0 1102 ]]></artwork> 1103 </figure> 1104 <t> 1105 The range decoder extracts the symbols and integers encoded using the range 1106 encoder in <xref target="range-encoder"/>. 1107 The range decoder maintains an internal state vector composed of the two-tuple 1108 (val, rng), representing the difference between the high end of the 1109 current range and the actual coded value, minus one, and the size of the 1110 current range, respectively. 1111 Both val and rng are 32-bit unsigned integer values. 1112 </t> 1113 1114 <section anchor="range-decoder-init" title="Range Decoder Initialization"> 1115 <t> 1116 Let b0 be the first input byte (or zero if there are no bytes in this Opus 1117 frame). 1118 The decoder initializes rng to 128 and initializes val to 1119 (127 - (b0>>1)), where (b0>>1) is the top 7 bits of the 1120 first input byte. 1121 It saves the remaining bit, (b0&1), for use in the renormalization 1122 procedure described in <xref target="range-decoder-renorm"/>, which the 1123 decoder invokes immediately after initialization to read additional bits and 1124 establish the invariant that rng > 2**23. 1125 </t> 1126 </section> 1127 1128 <section anchor="decoding-symbols" title="Decoding Symbols"> 1129 <t> 1130 Decoding a symbol is a two-step process. 1131 The first step determines a 16-bit unsigned value fs, which lies within the 1132 range of some symbol in the current context. 1133 The second step updates the range decoder state with the three-tuple 1134 (fl[k], fh[k], ft) corresponding to that symbol. 1135 </t> 1136 <t> 1137 The first step is implemented by ec_decode() (entdec.c), which computes 1138 <figure align="center"> 1139 <artwork align="center"><![CDATA[ 1140 val 1141 fs = ft - min(------ + 1, ft) . 1142 rng/ft 1143 ]]></artwork> 1144 </figure> 1145 The divisions here are integer division. 1146 </t> 1147 <t> 1148 The decoder then identifies the symbol in the current context corresponding to 1149 fs; i.e., the value of k whose three-tuple (fl[k], fh[k], ft) 1150 satisfies fl[k] <= fs < fh[k]. 1151 It uses this tuple to update val according to 1152 <figure align="center"> 1153 <artwork align="center"><![CDATA[ 1154 rng 1155 val = val - --- * (ft - fh[k]) . 1156 ft 1157 ]]></artwork> 1158 </figure> 1159 If fl[k] is greater than zero, then the decoder updates rng using 1160 <figure align="center"> 1161 <artwork align="center"><![CDATA[ 1162 rng 1163 rng = --- * (fh[k] - fl[k]) . 1164 ft 1165 ]]></artwork> 1166 </figure> 1167 Otherwise, it updates rng using 1168 <figure align="center"> 1169 <artwork align="center"><![CDATA[ 1170 rng 1171 rng = rng - --- * (ft - fh[k]) . 1172 ft 1173 ]]></artwork> 1174 </figure> 1175 </t> 1176 <t> 1177 Using a special case for the first symbol (rather than the last symbol, as is 1178 commonly done in other arithmetic coders) ensures that all the truncation 1179 error from the finite precision arithmetic accumulates in symbol 0. 1180 This makes the cost of coding a 0 slightly smaller, on average, than its 1181 estimated probability indicates and makes the cost of coding any other symbol 1182 slightly larger. 1183 When contexts are designed so that 0 is the most probable symbol, which is 1184 often the case, this strategy minimizes the inefficiency introduced by the 1185 finite precision. 1186 It also makes some of the special-case decoding routines in 1187 <xref target="decoding-alternate"/> particularly simple. 1188 </t> 1189 <t> 1190 After the updates, implemented by ec_dec_update() (entdec.c), the decoder 1191 normalizes the range using the procedure in the next section, and returns the 1192 index k. 1193 </t> 1194 1195 <section anchor="range-decoder-renorm" title="Renormalization"> 1196 <t> 1197 To normalize the range, the decoder repeats the following process, implemented 1198 by ec_dec_normalize() (entdec.c), until rng > 2**23. 1199 If rng is already greater than 2**23, the entire process is skipped. 1200 First, it sets rng to (rng<<8). 1201 Then it reads the next byte of the Opus frame and forms an 8-bit value sym, 1202 using the left-over bit buffered from the previous byte as the high bit 1203 and the top 7 bits of the byte just read as the other 7 bits of sym. 1204 The remaining bit in the byte just read is buffered for use in the next 1205 iteration. 1206 If no more input bytes remain, it uses zero bits instead. 1207 See <xref target="range-decoder-init"/> for the initialization used to process 1208 the first byte. 1209 Then, it sets 1210 <figure align="center"> 1211 <artwork align="center"><![CDATA[ 1212 val = ((val<<8) + (255-sym)) & 0x7FFFFFFF . 1213 ]]></artwork> 1214 </figure> 1215 </t> 1216 <t> 1217 It is normal and expected that the range decoder will read several bytes 1218 into the raw bits data (if any) at the end of the packet by the time the frame 1219 is completely decoded, as illustrated in <xref target="finalize-example"/>. 1220 This same data MUST also be returned as raw bits when requested. 1221 The encoder is expected to terminate the stream in such a way that the decoder 1222 will decode the intended values regardless of the data contained in the raw 1223 bits. 1224 <xref target="encoder-finalizing"/> describes a procedure for doing this. 1225 If the range decoder consumes all of the bytes belonging to the current frame, 1226 it MUST continue to use zero when any further input bytes are required, even 1227 if there is additional data in the current packet from padding or other 1228 frames. 1229 </t> 1230 1231 <figure anchor="finalize-example" title="Illustrative example of raw bits 1232 overlapping range coder data"> 1233 <artwork align="center"><![CDATA[ 1234 n n+1 n+2 n+3 1235 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 1236 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 1237 : | <----------- Overlap region ------------> | : 1238 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 1239 ^ ^ 1240 | End of data buffered by the range coder | 1241 ...-----------------------------------------------+ 1242 | 1243 | End of data consumed by raw bits 1244 +-------------------------------------------------------... 1245 ]]></artwork> 1246 </figure> 1247 </section> 1248 </section> 1249 1250 <section anchor="decoding-alternate" title="Alternate Decoding Methods"> 1251 <t> 1252 The reference implementation uses three additional decoding methods that are 1253 exactly equivalent to the above, but make assumptions and simplifications that 1254 allow for a more efficient implementation. 1255 </t> 1256 <section anchor="ec_decode_bin" title="ec_decode_bin()"> 1257 <t> 1258 The first is ec_decode_bin() (entdec.c), defined using the parameter ftb 1259 instead of ft. 1260 It is mathematically equivalent to calling ec_decode() with 1261 ft = (1<<ftb), but avoids one of the divisions. 1262 </t> 1263 </section> 1264 <section anchor="ec_dec_bit_logp" title="ec_dec_bit_logp()"> 1265 <t> 1266 The next is ec_dec_bit_logp() (entdec.c), which decodes a single binary symbol, 1267 replacing both the ec_decode() and ec_dec_update() steps. 1268 The context is described by a single parameter, logp, which is the absolute 1269 value of the base-2 logarithm of the probability of a "1". 1270 It is mathematically equivalent to calling ec_decode() with 1271 ft = (1<<logp), followed by ec_dec_update() with 1272 the 3-tuple (fl[k] = 0, 1273 fh[k] = (1<<logp) - 1, 1274 ft = (1<<logp)) if the returned value 1275 of fs is less than (1<<logp) - 1 (a "0" was decoded), and with 1276 (fl[k] = (1<<logp) - 1, 1277 fh[k] = ft = (1<<logp)) otherwise (a "1" was 1278 decoded). 1279 The implementation requires no multiplications or divisions. 1280 </t> 1281 </section> 1282 <section anchor="ec_dec_icdf" title="ec_dec_icdf()"> 1283 <t> 1284 The last is ec_dec_icdf() (entdec.c), which decodes a single symbol with a 1285 table-based context of up to 8 bits, also replacing both the ec_decode() and 1286 ec_dec_update() steps, as well as the search for the decoded symbol in between. 1287 The context is described by two parameters, an icdf 1288 ("inverse" cumulative distribution function) table and ftb. 1289 As with ec_decode_bin(), (1<<ftb) is equivalent to ft. 1290 idcf[k], on the other hand, stores (1<<ftb)-fh[k], which is equal to 1291 (1<<ftb) - fl[k+1]. 1292 fl[0] is assumed to be 0, and the table is terminated by a value of 0 (where 1293 fh[k] == ft). 1294 </t> 1295 <t> 1296 The function is mathematically equivalent to calling ec_decode() with 1297 ft = (1<<ftb), using the returned value fs to search the table 1298 for the first entry where fs < (1<<ftb)-icdf[k], and 1299 calling ec_dec_update() with 1300 fl[k] = (1<<ftb) - icdf[k-1] (or 0 1301 if k == 0), fh[k] = (1<<ftb) - idcf[k], 1302 and ft = (1<<ftb). 1303 Combining the search with the update allows the division to be replaced by a 1304 series of multiplications (which are usually much cheaper), and using an 1305 inverse CDF allows the use of an ftb as large as 8 in an 8-bit table without 1306 any special cases. 1307 This is the primary interface with the range decoder in the SILK layer, though 1308 it is used in a few places in the CELT layer as well. 1309 </t> 1310 <t> 1311 Although icdf[k] is more convenient for the code, the frequency counts, f[k], 1312 are a more natural representation of the probability distribution function 1313 (PDF) for a given symbol. 1314 Therefore this draft lists the latter, not the former, when describing the 1315 context in which a symbol is coded as a list, e.g., {4, 4, 4, 4}/16 for a 1316 uniform context with four possible values and ft = 16. 1317 The value of ft after the slash is always the sum of the entries in the PDF, 1318 but is included for convenience. 1319 Contexts with identical probabilities, f[k]/ft, but different values of ft 1320 (or equivalently, ftb) are not the same, and cannot, in general, be used in 1321 place of one another. 1322 An icdf table is also not capable of representing a PDF where the first symbol 1323 has 0 probability. 1324 In such contexts, ec_dec_icdf() can decode the symbol by using a table that 1325 drops the entries for any initial zero-probability values and adding the 1326 constant offset of the first value with a non-zero probability to its return 1327 value. 1328 </t> 1329 </section> 1330 </section> 1331 1332 <section anchor="decoding-bits" title="Decoding Raw Bits"> 1333 <t> 1334 The raw bits used by the CELT layer are packed at the end of the packet, with 1335 the least significant bit of the first value packed in the least significant 1336 bit of the last byte, filling up to the most significant bit in the last byte, 1337 continuing on to the least significant bit of the penultimate byte, and so on. 1338 The reference implementation reads them using ec_dec_bits() (entdec.c). 1339 Because the range decoder must read several bytes ahead in the stream, as 1340 described in <xref target="range-decoder-renorm"/>, the input consumed by the 1341 raw bits may overlap with the input consumed by the range coder, and a decoder 1342 MUST allow this. 1343 The format should render it impossible to attempt to read more raw bits than 1344 there are actual bits in the frame, though a decoder may wish to check for 1345 this and report an error. 1346 </t> 1347 </section> 1348 1349 <section anchor="ec_dec_uint" title="Decoding Uniformly Distributed Integers"> 1350 <t> 1351 The function ec_dec_uint() (entdec.c) decodes one of ft equiprobable values in 1352 the range 0 to (ft - 1), inclusive, each with a frequency of 1, 1353 where ft may be as large as (2**32 - 1). 1354 Because ec_decode() is limited to a total frequency of (2**16 - 1), 1355 it splits up the value into a range coded symbol representing up to 8 of the 1356 high bits, and, if necessary, raw bits representing the remainder of the 1357 value. 1358 The limit of 8 bits in the range coded symbol is a trade-off between 1359 implementation complexity, modeling error (since the symbols no longer truly 1360 have equal coding cost), and rounding error introduced by the range coder 1361 itself (which gets larger as more bits are included). 1362 Using raw bits reduces the maximum number of divisions required in the worst 1363 case, but means that it may be possible to decode a value outside the range 1364 0 to (ft - 1), inclusive. 1365 </t> 1366 1367 <t> 1368 ec_dec_uint() takes a single, positive parameter, ft, which is not necessarily 1369 a power of two, and returns an integer, t, whose value lies between 0 and 1370 (ft - 1), inclusive. 1371 Let ftb = ilog(ft - 1), i.e., the number of bits required 1372 to store (ft - 1) in two's complement notation. 1373 If ftb is 8 or less, then t is decoded with t = ec_decode(ft), and 1374 the range coder state is updated using the three-tuple (t, t + 1, 1375 ft). 1376 </t> 1377 <t> 1378 If ftb is greater than 8, then the top 8 bits of t are decoded using 1379 <figure align="center"> 1380 <artwork align="center"><![CDATA[ 1381 t = ec_decode(((ft - 1) >> (ftb - 8)) + 1) , 1382 ]]></artwork> 1383 </figure> 1384 the decoder state is updated using the three-tuple 1385 (t, t + 1, 1386 ((ft - 1) >> (ftb - 8)) + 1), 1387 and the remaining bits are decoded as raw bits, setting 1388 <figure align="center"> 1389 <artwork align="center"><![CDATA[ 1390 t = (t << (ftb - 8)) | ec_dec_bits(ftb - 8) . 1391 ]]></artwork> 1392 </figure> 1393 If, at this point, t >= ft, then the current frame is corrupt. 1394 In that case, the decoder should assume there has been an error in the coding, 1395 decoding, or transmission and SHOULD take measures to conceal the 1396 error and/or report to the application that the error has occurred. 1397 </t> 1398 1399 </section> 1400 1401 <section anchor="decoder-tell" title="Current Bit Usage"> 1402 <t> 1403 The bit allocation routines in the CELT decoder need a conservative upper bound 1404 on the number of bits that have been used from the current frame thus far, 1405 including both range coder bits and raw bits. 1406 This drives allocation decisions that must match those made in the encoder. 1407 The upper bound is computed in the reference implementation to whole-bit 1408 precision by the function ec_tell() (entcode.h) and to fractional 1/8th bit 1409 precision by the function ec_tell_frac() (entcode.c). 1410 Like all operations in the range coder, it must be implemented in a bit-exact 1411 manner, and must produce exactly the same value returned by the same functions 1412 in the encoder after encoding the same symbols. 1413 </t> 1414 <t> 1415 ec_tell() is guaranteed to return ceil(ec_tell_frac()/8.0). 1416 In various places the codec will check to ensure there is enough room to 1417 contain a symbol before attempting to decode it. 1418 In practice, although the number of bits used so far is an upper bound, 1419 decoding a symbol whose probability model suggests it has a worst-case cost of 1420 p 1/8th bits may actually advance the return value of ec_tell_frac() by 1421 p-1, p, or p+1 1/8th bits, due to approximation error in that upper bound, 1422 truncation error in the range coder, and for large values of ft, modeling 1423 error in ec_dec_uint(). 1424 </t> 1425 <t> 1426 However, this error is bounded, and periodic calls to ec_tell() or 1427 ec_tell_frac() at precisely defined points in the decoding process prevent it 1428 from accumulating. 1429 For a range coder symbol that requires a whole number of bits (i.e., 1430 for which ft/(fh[k] - fl[k]) is a power of two), where there are at 1431 least p 1/8th bits available, decoding the symbol will never cause ec_tell() or 1432 ec_tell_frac() to exceed the size of the frame ("bust the budget"). 1433 In this case the return value of ec_tell_frac() will only advance by more than 1434 p 1/8th bits if there was an additional, fractional number of bits remaining, 1435 and it will never advance beyond the next whole-bit boundary, which is safe, 1436 since frames always contain a whole number of bits. 1437 However, when p is not a whole number of bits, an extra 1/8th bit is required 1438 to ensure that decoding the symbol will not bust the budget. 1439 </t> 1440 <t> 1441 The reference implementation keeps track of the total number of whole bits that 1442 have been processed by the decoder so far in the variable nbits_total, 1443 including the (possibly fractional) number of bits that are currently 1444 buffered, but not consumed, inside the range coder. 1445 nbits_total is initialized to 9 just before the initial range renormalization 1446 process completes (or equivalently, it can be initialized to 33 after the 1447 first renormalization). 1448 The extra two bits over the actual amount buffered by the range coder 1449 guarantees that it is an upper bound and that there is enough room for the 1450 encoder to terminate the stream. 1451 Each iteration through the range coder's renormalization loop increases 1452 nbits_total by 8. 1453 Reading raw bits increases nbits_total by the number of raw bits read. 1454 </t> 1455 1456 <section anchor="ec_tell" title="ec_tell()"> 1457 <t> 1458 The whole number of bits buffered in rng may be estimated via lg = ilog(rng). 1459 ec_tell() then becomes a simple matter of removing these bits from the total. 1460 It returns (nbits_total - lg). 1461 </t> 1462 <t> 1463 In a newly initialized decoder, before any symbols have been read, this reports 1464 that 1 bit has been used. 1465 This is the bit reserved for termination of the encoder. 1466 </t> 1467 </section> 1468 1469 <section anchor="ec_tell_frac" title="ec_tell_frac()"> 1470 <t> 1471 ec_tell_frac() estimates the number of bits buffered in rng to fractional 1472 precision. 1473 Since rng must be greater than 2**23 after renormalization, lg must be at least 1474 24. 1475 Let 1476 <figure align="center"> 1477 <artwork align="center"> 1478 <![CDATA[ 1479 r_Q15 = rng >> (lg-16) , 1480 ]]></artwork> 1481 </figure> 1482 so that 32768 <= r_Q15 < 65536, an unsigned Q15 value representing the 1483 fractional part of rng. 1484 Then the following procedure can be used to add one bit of precision to lg. 1485 First, update 1486 <figure align="center"> 1487 <artwork align="center"> 1488 <![CDATA[ 1489 r_Q15 = (r_Q15*r_Q15) >> 15 . 1490 ]]></artwork> 1491 </figure> 1492 Then add the 16th bit of r_Q15 to lg via 1493 <figure align="center"> 1494 <artwork align="center"> 1495 <![CDATA[ 1496 lg = 2*lg + (r_Q15 >> 16) . 1497 ]]></artwork> 1498 </figure> 1499 Finally, if this bit was a 1, reduce r_Q15 by a factor of two via 1500 <figure align="center"> 1501 <artwork align="center"> 1502 <![CDATA[ 1503 r_Q15 = r_Q15 >> 1 , 1504 ]]></artwork> 1505 </figure> 1506 so that it once again lies in the range 32768 <= r_Q15 < 65536. 1507 </t> 1508 <t> 1509 This procedure is repeated three times to extend lg to 1/8th bit precision. 1510 ec_tell_frac() then returns (nbits_total*8 - lg). 1511 </t> 1512 </section> 1513 1514 </section> 1515 1516 </section> 1517 1518 <section anchor="silk_decoder_outline" title="SILK Decoder"> 1519 <t> 1520 The decoder's LP layer uses a modified version of the SILK codec (herein simply 1521 called "SILK"), which runs a decoded excitation signal through adaptive 1522 long-term and short-term prediction synthesis filters. 1523 It runs at NB, MB, and WB sample rates internally. 1524 When used in a SWB or FB Hybrid frame, the LP layer itself still only runs in 1525 WB. 1526 </t> 1527 1528 <section title="SILK Decoder Modules"> 1529 <t> 1530 An overview of the decoder is given in <xref target="silk_decoder_figure"/>. 1531 </t> 1532 <figure align="center" anchor="silk_decoder_figure" title="SILK Decoder"> 1533 <artwork align="center"> 1534 <![CDATA[ 1535 +---------+ +------------+ 1536 -->| Range |--->| Decode |---------------------------+ 1537 1 | Decoder | 2 | Parameters |----------+ 5 | 1538 +---------+ +------------+ 4 | | 1539 3 | | | 1540 \/ \/ \/ 1541 +------------+ +------------+ +------------+ 1542 | Generate |-->| LTP |-->| LPC | 1543 | Excitation | | Synthesis | | Synthesis | 1544 +------------+ +------------+ +------------+ 1545 ^ | 1546 | | 1547 +-------------------+----------------+ 1548 | 6 1549 | +------------+ +-------------+ 1550 +-->| Stereo |-->| Sample Rate |--> 1551 | Unmixing | 7 | Conversion | 8 1552 +------------+ +-------------+ 1553 1554 1: Range encoded bitstream 1555 2: Coded parameters 1556 3: Pulses, LSBs, and signs 1557 4: Pitch lags, Long-Term Prediction (LTP) coefficients 1558 5: Linear Predictive Coding (LPC) coefficients and gains 1559 6: Decoded signal (mono or mid-side stereo) 1560 7: Unmixed signal (mono or left-right stereo) 1561 8: Resampled signal 1562 ]]> 1563 </artwork> 1564 </figure> 1565 1566 <t> 1567 The decoder feeds the bitstream (1) to the range decoder from 1568 <xref target="range-decoder"/>, and then decodes the parameters in it (2) 1569 using the procedures detailed in 1570 Sections <xref format="counter" target="silk_header_bits"/> 1571 through <xref format="counter" target="silk_signs"/>. 1572 These parameters (3, 4, 5) are used to generate an excitation signal (see 1573 <xref target="silk_excitation_reconstruction"/>), which is fed to an optional 1574 long-term prediction (LTP) filter (voiced frames only, see 1575 <xref target="silk_ltp_synthesis"/>) and then a short-term prediction filter 1576 (see <xref target="silk_lpc_synthesis"/>), producing the decoded signal (6). 1577 For stereo streams, the mid-side representation is converted to separate left 1578 and right channels (7). 1579 The result is finally resampled to the desired output sample rate (e.g., 1580 48 kHz) so that the resampled signal (8) can be mixed with the CELT 1581 layer. 1582 </t> 1583 1584 </section> 1585 1586 <section anchor="silk_layer_organization" title="LP Layer Organization"> 1587 1588 <t> 1589 Internally, the LP layer of a single Opus frame is composed of either a single 1590 10 ms regular SILK frame or between one and three 20 ms regular SILK 1591 frames. 1592 A stereo Opus frame may double the number of regular SILK frames (up to a total 1593 of six), since it includes separate frames for a mid channel and, optionally, 1594 a side channel. 1595 Optional Low Bit-Rate Redundancy (LBRR) frames, which are reduced-bitrate 1596 encodings of previous SILK frames, may be included to aid in recovery from 1597 packet loss. 1598 If present, these appear before the regular SILK frames. 1599 They are in most respects identical to regular, active SILK frames, except that 1600 they are usually encoded with a lower bitrate. 1601 This draft uses "SILK frame" to refer to either one and "regular SILK frame" if 1602 it needs to draw a distinction between the two. 1603 </t> 1604 <t> 1605 Logically, each SILK frame is in turn composed of either two or four 5 ms 1606 subframes. 1607 Various parameters, such as the quantization gain of the excitation and the 1608 pitch lag and filter coefficients can vary on a subframe-by-subframe basis. 1609 Physically, the parameters for each subframe are interleaved in the bitstream, 1610 as described in the relevant sections for each parameter. 1611 </t> 1612 <t> 1613 All of these frames and subframes are decoded from the same range coder, with 1614 no padding between them. 1615 Thus packing multiple SILK frames in a single Opus frame saves, on average, 1616 half a byte per SILK frame. 1617 It also allows some parameters to be predicted from prior SILK frames in the 1618 same Opus frame, since this does not degrade packet loss robustness (beyond 1619 any penalty for merely using fewer, larger packets to store multiple frames). 1620 </t> 1621 1622 <t> 1623 Stereo support in SILK uses a variant of mid-side coding, allowing a mono 1624 decoder to simply decode the mid channel. 1625 However, the data for the two channels is interleaved, so a mono decoder must 1626 still unpack the data for the side channel. 1627 It would be required to do so anyway for Hybrid Opus frames, or to support 1628 decoding individual 20 ms frames. 1629 </t> 1630 1631 <t> 1632 <xref target="silk_symbols"/> summarizes the overall grouping of the contents of 1633 the LP layer. 1634 Figures <xref format="counter" target="silk_mono_60ms_frame"/> 1635 and <xref format="counter" target="silk_stereo_60ms_frame"/> illustrate 1636 the ordering of the various SILK frames for a 60 ms Opus frame, for both 1637 mono and stereo, respectively. 1638 </t> 1639 1640 <texttable anchor="silk_symbols" 1641 title="Organization of the SILK layer of an Opus frame"> 1642 <ttcol align="center">Symbol(s)</ttcol> 1643 <ttcol align="center">PDF(s)</ttcol> 1644 <ttcol align="center">Condition</ttcol> 1645 1646 <c>Voice Activity Detection (VAD) flags</c> 1647 <c>{1, 1}/2</c> 1648 <c/> 1649 1650 <c>LBRR flag</c> 1651 <c>{1, 1}/2</c> 1652 <c/> 1653 1654 <c>Per-frame LBRR flags</c> 1655 <c><xref target="silk_lbrr_flag_pdfs"/></c> 1656 <c><xref target="silk_lbrr_flags"/></c> 1657 1658 <c>LBRR Frame(s)</c> 1659 <c><xref target="silk_frame"/></c> 1660 <c><xref target="silk_lbrr_flags"/></c> 1661 1662 <c>Regular SILK Frame(s)</c> 1663 <c><xref target="silk_frame"/></c> 1664 <c/> 1665 1666 </texttable> 1667 1668 <figure align="center" anchor="silk_mono_60ms_frame" 1669 title="A 60 ms Mono Frame"> 1670 <artwork align="center"><![CDATA[ 1671 +---------------------------------+ 1672 | VAD Flags | 1673 +---------------------------------+ 1674 | LBRR Flag | 1675 +---------------------------------+ 1676 | Per-Frame LBRR Flags (Optional) | 1677 +---------------------------------+ 1678 | LBRR Frame 1 (Optional) | 1679 +---------------------------------+ 1680 | LBRR Frame 2 (Optional) | 1681 +---------------------------------+ 1682 | LBRR Frame 3 (Optional) | 1683 +---------------------------------+ 1684 | Regular SILK Frame 1 | 1685 +---------------------------------+ 1686 | Regular SILK Frame 2 | 1687 +---------------------------------+ 1688 | Regular SILK Frame 3 | 1689 +---------------------------------+ 1690 ]]></artwork> 1691 </figure> 1692 1693 <figure align="center" anchor="silk_stereo_60ms_frame" 1694 title="A 60 ms Stereo Frame"> 1695 <artwork align="center"><![CDATA[ 1696 +---------------------------------------+ 1697 | Mid VAD Flags | 1698 +---------------------------------------+ 1699 | Mid LBRR Flag | 1700 +---------------------------------------+ 1701 | Side VAD Flags | 1702 +---------------------------------------+ 1703 | Side LBRR Flag | 1704 +---------------------------------------+ 1705 | Mid Per-Frame LBRR Flags (Optional) | 1706 +---------------------------------------+ 1707 | Side Per-Frame LBRR Flags (Optional) | 1708 +---------------------------------------+ 1709 | Mid LBRR Frame 1 (Optional) | 1710 +---------------------------------------+ 1711 | Side LBRR Frame 1 (Optional) | 1712 +---------------------------------------+ 1713 | Mid LBRR Frame 2 (Optional) | 1714 +---------------------------------------+ 1715 | Side LBRR Frame 2 (Optional) | 1716 +---------------------------------------+ 1717 | Mid LBRR Frame 3 (Optional) | 1718 +---------------------------------------+ 1719 | Side LBRR Frame 3 (Optional) | 1720 +---------------------------------------+ 1721 | Mid Regular SILK Frame 1 | 1722 +---------------------------------------+ 1723 | Side Regular SILK Frame 1 (Optional) | 1724 +---------------------------------------+ 1725 | Mid Regular SILK Frame 2 | 1726 +---------------------------------------+ 1727 | Side Regular SILK Frame 2 (Optional) | 1728 +---------------------------------------+ 1729 | Mid Regular SILK Frame 3 | 1730 +---------------------------------------+ 1731 | Side Regular SILK Frame 3 (Optional) | 1732 +---------------------------------------+ 1733 ]]></artwork> 1734 </figure> 1735 1736 </section> 1737 1738 <section anchor="silk_header_bits" title="Header Bits"> 1739 <t> 1740 The LP layer begins with two to eight header bits, decoded in silk_Decode() 1741 (dec_API.c). 1742 These consist of one Voice Activity Detection (VAD) bit per frame (up to 3), 1743 followed by a single flag indicating the presence of LBRR frames. 1744 For a stereo packet, these first flags correspond to the mid channel, and a 1745 second set of flags is included for the side channel. 1746 </t> 1747 <t> 1748 Because these are the first symbols decoded by the range coder and because they 1749 are coded as binary values with uniform probability, they can be extracted 1750 directly from the most significant bits of the first byte of compressed data. 1751 Thus, a receiver can determine if an Opus frame contains any active SILK frames 1752 without the overhead of using the range decoder. 1753 </t> 1754 </section> 1755 1756 <section anchor="silk_lbrr_flags" title="Per-Frame LBRR Flags"> 1757 <t> 1758 For Opus frames longer than 20 ms, a set of LBRR flags is 1759 decoded for each channel that has its LBRR flag set. 1760 Each set contains one flag per 20 ms SILK frame. 1761 40 ms Opus frames use the 2-frame LBRR flag PDF from 1762 <xref target="silk_lbrr_flag_pdfs"/>, and 60 ms Opus frames use the 1763 3-frame LBRR flag PDF. 1764 For each channel, the resulting 2- or 3-bit integer contains the corresponding 1765 LBRR flag for each frame, packed in order from the LSB to the MSB. 1766 </t> 1767 1768 <texttable anchor="silk_lbrr_flag_pdfs" title="LBRR Flag PDFs"> 1769 <ttcol>Frame Size</ttcol> 1770 <ttcol>PDF</ttcol> 1771 <c>40 ms</c> <c>{0, 53, 53, 150}/256</c> 1772 <c>60 ms</c> <c>{0, 41, 20, 29, 41, 15, 28, 82}/256</c> 1773 </texttable> 1774 1775 <t> 1776 A 10 or 20 ms Opus frame does not contain any per-frame LBRR flags, 1777 as there may be at most one LBRR frame per channel. 1778 The global LBRR flag in the header bits (see <xref target="silk_header_bits"/>) 1779 is already sufficient to indicate the presence of that single LBRR frame. 1780 </t> 1781 1782 </section> 1783 1784 <section anchor="silk_lbrr_frames" title="LBRR Frames"> 1785 <t> 1786 The LBRR frames, if present, contain an encoded representation of the signal 1787 immediately prior to the current Opus frame as if it were encoded with the 1788 current mode, frame size, audio bandwidth, and channel count, even if those 1789 differ from the prior Opus frame. 1790 When one of these parameters changes from one Opus frame to the next, this 1791 implies that the LBRR frames of the current Opus frame may not be simple 1792 drop-in replacements for the contents of the previous Opus frame. 1793 </t> 1794 1795 <t> 1796 For example, when switching from 20 ms to 60 ms, the 60 ms Opus 1797 frame may contain LBRR frames covering up to three prior 20 ms Opus 1798 frames, even if those frames already contained LBRR frames covering some of 1799 the same time periods. 1800 When switching from 20 ms to 10 ms, the 10 ms Opus frame can 1801 contain an LBRR frame covering at most half the prior 20 ms Opus frame, 1802 potentially leaving a hole that needs to be concealed from even a single 1803 packet loss (see <xref target="Packet Loss Concealment"/>). 1804 When switching from mono to stereo, the LBRR frames in the first stereo Opus 1805 frame MAY contain a non-trivial side channel. 1806 </t> 1807 1808 <t> 1809 In order to properly produce LBRR frames under all conditions, an encoder might 1810 need to buffer up to 60 ms of audio and re-encode it during these 1811 transitions. 1812 However, the reference implementation opts to disable LBRR frames at the 1813 transition point for simplicity. 1814 Since transitions are relatively infrequent in normal usage, this does not have 1815 a significant impact on packet loss robustness. 1816 </t> 1817 1818 <t> 1819 The LBRR frames immediately follow the LBRR flags, prior to any regular SILK 1820 frames. 1821 <xref target="silk_frame"/> describes their exact contents. 1822 LBRR frames do not include their own separate VAD flags. 1823 LBRR frames are only meant to be transmitted for active speech, thus all LBRR 1824 frames are treated as active. 1825 </t> 1826 1827 <t> 1828 In a stereo Opus frame longer than 20 ms, although the per-frame LBRR 1829 flags for the mid channel are coded as a unit before the per-frame LBRR flags 1830 for the side channel, the LBRR frames themselves are interleaved. 1831 The decoder parses an LBRR frame for the mid channel of a given 20 ms 1832 interval (if present) and then immediately parses the corresponding LBRR 1833 frame for the side channel (if present), before proceeding to the next 1834 20 ms interval. 1835 </t> 1836 </section> 1837 1838 <section anchor="silk_regular_frames" title="Regular SILK Frames"> 1839 <t> 1840 The regular SILK frame(s) follow the LBRR frames (if any). 1841 <xref target="silk_frame"/> describes their contents, as well. 1842 Unlike the LBRR frames, a regular SILK frame is coded for each time interval in 1843 an Opus frame, even if the corresponding VAD flags are unset. 1844 For stereo Opus frames longer than 20 ms, the regular mid and side SILK 1845 frames for each 20 ms interval are interleaved, just as with the LBRR 1846 frames. 1847 The side frame may be skipped by coding an appropriate flag, as detailed in 1848 <xref target="silk_mid_only_flag"/>. 1849 </t> 1850 </section> 1851 1852 <section anchor="silk_frame" title="SILK Frame Contents"> 1853 <t> 1854 Each SILK frame includes a set of side information that encodes 1855 <list style="symbols"> 1856 <t>The frame type and quantization type (<xref target="silk_frame_type"/>),</t> 1857 <t>Quantization gains (<xref target="silk_gains"/>),</t> 1858 <t>Short-term prediction filter coefficients (<xref target="silk_nlsfs"/>),</t> 1859 <t>A Line Spectral Frequencies (LSF) interpolation weight (<xref target="silk_nlsf_interpolation"/>),</t> 1860 <t> 1861 Long-term prediction filter lags and gains (<xref target="silk_ltp_params"/>), 1862 and 1863 </t> 1864 <t>A linear congruential generator (LCG) seed (<xref target="silk_seed"/>).</t> 1865 </list> 1866 The quantized excitation signal (see <xref target="silk_excitation"/>) follows 1867 these at the end of the frame. 1868 <xref target="silk_frame_symbols"/> details the overall organization of a 1869 SILK frame. 1870 </t> 1871 1872 <texttable anchor="silk_frame_symbols" 1873 title="Order of the symbols in an individual SILK frame"> 1874 <ttcol align="center">Symbol(s)</ttcol> 1875 <ttcol align="center">PDF(s)</ttcol> 1876 <ttcol align="center">Condition</ttcol> 1877 1878 <c>Stereo Prediction Weights</c> 1879 <c><xref target="silk_stereo_pred_pdfs"/></c> 1880 <c><xref target="silk_stereo_pred"/></c> 1881 1882 <c>Mid-only Flag</c> 1883 <c><xref target="silk_mid_only_pdf"/></c> 1884 <c><xref target="silk_mid_only_flag"/></c> 1885 1886 <c>Frame Type</c> 1887 <c><xref target="silk_frame_type"/></c> 1888 <c/> 1889 1890 <c>Subframe Gains</c> 1891 <c><xref target="silk_gains"/></c> 1892 <c/> 1893 1894 <c>Normalized LSF Stage-1 Index</c> 1895 <c><xref target="silk_nlsf_stage1_pdfs"/></c> 1896 <c/> 1897 1898 <c>Normalized LSF Stage-2 Residual</c> 1899 <c><xref target="silk_nlsf_stage2"/></c> 1900 <c/> 1901 1902 <c>Normalized LSF Interpolation Weight</c> 1903 <c><xref target="silk_nlsf_interp_pdf"/></c> 1904 <c>20 ms frame</c> 1905 1906 <c>Primary Pitch Lag</c> 1907 <c><xref target="silk_ltp_lags"/></c> 1908 <c>Voiced frame</c> 1909 1910 <c>Subframe Pitch Contour</c> 1911 <c><xref target="silk_pitch_contour_pdfs"/></c> 1912 <c>Voiced frame</c> 1913 1914 <c>Periodicity Index</c> 1915 <c><xref target="silk_perindex_pdf"/></c> 1916 <c>Voiced frame</c> 1917 1918 <c>LTP Filter</c> 1919 <c><xref target="silk_ltp_filter_pdfs"/></c> 1920 <c>Voiced frame</c> 1921 1922 <c>LTP Scaling</c> 1923 <c><xref target="silk_ltp_scaling_pdf"/></c> 1924 <c><xref target="silk_ltp_scaling"/></c> 1925 1926 <c>LCG Seed</c> 1927 <c><xref target="silk_seed_pdf"/></c> 1928 <c/> 1929 1930 <c>Excitation Rate Level</c> 1931 <c><xref target="silk_rate_level_pdfs"/></c> 1932 <c/> 1933 1934 <c>Excitation Pulse Counts</c> 1935 <c><xref target="silk_pulse_count_pdfs"/></c> 1936 <c/> 1937 1938 <c>Excitation Pulse Locations</c> 1939 <c><xref target="silk_pulse_locations"/></c> 1940 <c>Non-zero pulse count</c> 1941 1942 <c>Excitation LSBs</c> 1943 <c><xref target="silk_shell_lsb_pdf"/></c> 1944 <c><xref target="silk_pulse_counts"/></c> 1945 1946 <c>Excitation Signs</c> 1947 <c><xref target="silk_sign_pdfs"/></c> 1948 <c/> 1949 1950 </texttable> 1951 1952 <section anchor="silk_stereo_pred" toc="include" 1953 title="Stereo Prediction Weights"> 1954 <t> 1955 A SILK frame corresponding to the mid channel of a stereo Opus frame begins 1956 with a pair of side channel prediction weights, designed such that zeros 1957 indicate normal mid-side coupling. 1958 Since these weights can change on every frame, the first portion of each frame 1959 linearly interpolates between the previous weights and the current ones, using 1960 zeros for the previous weights if none are available. 1961 These prediction weights are never included in a mono Opus frame, and the 1962 previous weights are reset to zeros on any transition from mono to stereo. 1963 They are also not included in an LBRR frame for the side channel, even if the 1964 LBRR flags indicate the corresponding mid channel was not coded. 1965 In that case, the previous weights are used, again substituting in zeros if no 1966 previous weights are available since the last decoder reset 1967 (see <xref target="decoder-reset"/>). 1968 </t> 1969 1970 <t> 1971 To summarize, these weights are coded if and only if 1972 <list style="symbols"> 1973 <t>This is a stereo Opus frame (<xref target="toc_byte"/>), and</t> 1974 <t>The current SILK frame corresponds to the mid channel.</t> 1975 </list> 1976 </t> 1977 1978 <t> 1979 The prediction weights are coded in three separate pieces, which are decoded 1980 by silk_stereo_decode_pred() (decode_stereo_pred.c). 1981 The first piece jointly codes the high-order part of a table index for both 1982 weights. 1983 The second piece codes the low-order part of each table index. 1984 The third piece codes an offset used to linearly interpolate between table 1985 indices. 1986 The details are as follows. 1987 </t> 1988 1989 <t> 1990 Let n be an index decoded with the 25-element stage-1 PDF in 1991 <xref target="silk_stereo_pred_pdfs"/>. 1992 Then let i0 and i1 be indices decoded with the stage-2 and stage-3 PDFs in 1993 <xref target="silk_stereo_pred_pdfs"/>, respectively, and let i2 and i3 1994 be two more indices decoded with the stage-2 and stage-3 PDFs, all in that 1995 order. 1996 </t> 1997 1998 <texttable anchor="silk_stereo_pred_pdfs" title="Stereo Weight PDFs"> 1999 <ttcol align="left">Stage</ttcol> 2000 <ttcol align="left">PDF</ttcol> 2001 <c>Stage 1</c> 2002 <c>{7, 2, 1, 1, 1, 2003 10, 24, 8, 1, 1, 2004 3, 23, 92, 23, 3, 2005 1, 1, 8, 24, 10, 2006 1, 1, 1, 2, 7}/256</c> 2007 2008 <c>Stage 2</c> 2009 <c>{85, 86, 85}/256</c> 2010 2011 <c>Stage 3</c> 2012 <c>{51, 51, 52, 51, 51}/256</c> 2013 </texttable> 2014 2015 <t> 2016 Then use n, i0, and i2 to form two table indices, wi0 and wi1, according to 2017 <figure align="center"> 2018 <artwork align="center"><![CDATA[ 2019 wi0 = i0 + 3*(n/5) 2020 wi1 = i2 + 3*(n%5) 2021 ]]></artwork> 2022 </figure> 2023 where the division is integer division. 2024 The range of these indices is 0 to 14, inclusive. 2025 Let w[i] be the i'th weight from <xref target="silk_stereo_weights_table"/>. 2026 Then the two prediction weights, w0_Q13 and w1_Q13, are 2027 <figure align="center"> 2028 <artwork align="center"><![CDATA[ 2029 w1_Q13 = w_Q13[wi1] 2030 + ((w_Q13[wi1+1] - w_Q13[wi1])*6554) >> 16)*(2*i3 + 1) 2031 2032 w0_Q13 = w_Q13[wi0] 2033 + ((w_Q13[wi0+1] - w_Q13[wi0])*6554) >> 16)*(2*i1 + 1) 2034 - w1_Q13 2035 ]]></artwork> 2036 </figure> 2037 N.b., w1_Q13 is computed first here, because w0_Q13 depends on it. 2038 The constant 6554 is approximately 0.1 in Q16. 2039 Although wi0 and wi1 only have 15 possible values, 2040 <xref target="silk_stereo_weights_table"/> contains 16 entries to allow 2041 interpolation between entry wi0 and (wi0 + 1) (and likewise for wi1). 2042 </t> 2043 2044 <texttable anchor="silk_stereo_weights_table" 2045 title="Stereo Weight Table"> 2046 <ttcol align="left">Index</ttcol> 2047 <ttcol align="right">Weight (Q13)</ttcol> 2048 <c>0</c> <c>-13732</c> 2049 <c>1</c> <c>-10050</c> 2050 <c>2</c> <c>-8266</c> 2051 <c>3</c> <c>-7526</c> 2052 <c>4</c> <c>-6500</c> 2053 <c>5</c> <c>-5000</c> 2054 <c>6</c> <c>-2950</c> 2055 <c>7</c> <c>-820</c> 2056 <c>8</c> <c>820</c> 2057 <c>9</c> <c>2950</c> 2058 <c>10</c> <c>5000</c> 2059 <c>11</c> <c>6500</c> 2060 <c>12</c> <c>7526</c> 2061 <c>13</c> <c>8266</c> 2062 <c>14</c> <c>10050</c> 2063 <c>15</c> <c>13732</c> 2064 </texttable> 2065 2066 </section> 2067 2068 <section anchor="silk_mid_only_flag" toc="include" title="Mid-only Flag"> 2069 <t> 2070 A flag appears after the stereo prediction weights that indicates if only the 2071 mid channel is coded for this time interval. 2072 It appears only when 2073 <list style="symbols"> 2074 <t>This is a stereo Opus frame (see <xref target="toc_byte"/>),</t> 2075 <t>The current SILK frame corresponds to the mid channel, and</t> 2076 <t>Either 2077 <list style="symbols"> 2078 <t>This is a regular SILK frame where the VAD flags 2079 (see <xref target="silk_header_bits"/>) indicate that the corresponding side 2080 channel is not active.</t> 2081 <t> 2082 This is an LBRR frame where the LBRR flags 2083 (see <xref target="silk_header_bits"/> and <xref target="silk_lbrr_flags"/>) 2084 indicate that the corresponding side channel is not coded. 2085 </t> 2086 </list> 2087 </t> 2088 </list> 2089 It is omitted when there are no stereo weights, for all of the same reasons. 2090 It is also omitted for a regular SILK frame when the VAD flag of the 2091 corresponding side channel frame is set (indicating it is active). 2092 The side channel must be coded in this case, making the mid-only flag 2093 redundant. 2094 It is also omitted for an LBRR frame when the corresponding LBRR flags 2095 indicate the side channel is coded. 2096 </t> 2097 2098 <t> 2099 When the flag is present, the decoder reads a single value using the PDF in 2100 <xref target="silk_mid_only_pdf"/>, as implemented in 2101 silk_stereo_decode_mid_only() (decode_stereo_pred.c). 2102 If the flag is set, then there is no corresponding SILK frame for the side 2103 channel, the entire decoding process for the side channel is skipped, and 2104 zeros are fed to the stereo unmixing process (see 2105 <xref target="silk_stereo_unmixing"/>) instead. 2106 As stated above, LBRR frames still include this flag when the LBRR flag 2107 indicates that the side channel is not coded. 2108 In that case, if this flag is zero (indicating that there should be a side 2109 channel), then Packet Loss Concealment (PLC, see 2110 <xref target="Packet Loss Concealment"/>) SHOULD be invoked to recover a 2111 side channel signal. 2112 Otherwise, the stereo image will collapse. 2113 </t> 2114 2115 <texttable anchor="silk_mid_only_pdf" title="Mid-only Flag PDF"> 2116 <ttcol align="left">PDF</ttcol> 2117 <c>{192, 64}/256</c> 2118 </texttable> 2119 2120 </section> 2121 2122 <section anchor="silk_frame_type" toc="include" title="Frame Type"> 2123 <t> 2124 Each SILK frame contains a single "frame type" symbol that jointly codes the 2125 signal type and quantization offset type of the corresponding frame. 2126 If the current frame is a regular SILK frame whose VAD bit was not set (an 2127 "inactive" frame), then the frame type symbol takes on a value of either 0 or 2128 1 and is decoded using the first PDF in <xref target="silk_frame_type_pdfs"/>. 2129 If the frame is an LBRR frame or a regular SILK frame whose VAD flag was set 2130 (an "active" frame), then the value of the symbol may range from 2 to 5, 2131 inclusive, and is decoded using the second PDF in 2132 <xref target="silk_frame_type_pdfs"/>. 2133 <xref target="silk_frame_type_table"/> translates between the value of the 2134 frame type symbol and the corresponding signal type and quantization offset 2135 type. 2136 </t> 2137 2138 <texttable anchor="silk_frame_type_pdfs" title="Frame Type PDFs"> 2139 <ttcol>VAD Flag</ttcol> 2140 <ttcol>PDF</ttcol> 2141 <c>Inactive</c> <c>{26, 230, 0, 0, 0, 0}/256</c> 2142 <c>Active</c> <c>{0, 0, 24, 74, 148, 10}/256</c> 2143 </texttable> 2144 2145 <texttable anchor="silk_frame_type_table" 2146 title="Signal Type and Quantization Offset Type from Frame Type"> 2147 <ttcol>Frame Type</ttcol> 2148 <ttcol>Signal Type</ttcol> 2149 <ttcol align="right">Quantization Offset Type</ttcol> 2150 <c>0</c> <c>Inactive</c> <c>Low</c> 2151 <c>1</c> <c>Inactive</c> <c>High</c> 2152 <c>2</c> <c>Unvoiced</c> <c>Low</c> 2153 <c>3</c> <c>Unvoiced</c> <c>High</c> 2154 <c>4</c> <c>Voiced</c> <c>Low</c> 2155 <c>5</c> <c>Voiced</c> <c>High</c> 2156 </texttable> 2157 2158 </section> 2159 2160 <section anchor="silk_gains" toc="include" title="Subframe Gains"> 2161 <t> 2162 A separate quantization gain is coded for each 5 ms subframe. 2163 These gains control the step size between quantization levels of the excitation 2164 signal and, therefore, the quality of the reconstruction. 2165 They are independent of and unrelated to the pitch contours coded for voiced 2166 frames. 2167 The quantization gains are themselves uniformly quantized to 6 bits on a 2168 log scale, giving them a resolution of approximately 1.369 dB and a range 2169 of approximately 1.94 dB to 88.21 dB. 2170 </t> 2171 <t> 2172 The subframe gains are either coded independently, or relative to the gain from 2173 the most recent coded subframe in the same channel. 2174 Independent coding is used if and only if 2175 <list style="symbols"> 2176 <t> 2177 This is the first subframe in the current SILK frame, and 2178 </t> 2179 <t>Either 2180 <list style="symbols"> 2181 <t> 2182 This is the first SILK frame of its type (LBRR or regular) for this channel in 2183 the current Opus frame, or 2184 </t> 2185 <t> 2186 The previous SILK frame of the same type (LBRR or regular) for this channel in 2187 the same Opus frame was not coded. 2188 </t> 2189 </list> 2190 </t> 2191 </list> 2192 </t> 2193 2194 <t> 2195 In an independently coded subframe gain, the 3 most significant bits of the 2196 quantization gain are decoded using a PDF selected from 2197 <xref target="silk_independent_gain_msb_pdfs"/> based on the decoded signal 2198 type (see <xref target="silk_frame_type"/>). 2199 </t> 2200 2201 <texttable anchor="silk_independent_gain_msb_pdfs" 2202 title="PDFs for Independent Quantization Gain MSB Coding"> 2203 <ttcol align="left">Signal Type</ttcol> 2204 <ttcol align="left">PDF</ttcol> 2205 <c>Inactive</c> <c>{32, 112, 68, 29, 12, 1, 1, 1}/256</c> 2206 <c>Unvoiced</c> <c>{2, 17, 45, 60, 62, 47, 19, 4}/256</c> 2207 <c>Voiced</c> <c>{1, 3, 26, 71, 94, 50, 9, 2}/256</c> 2208 </texttable> 2209 2210 <t> 2211 The 3 least significant bits are decoded using a uniform PDF: 2212 </t> 2213 <texttable anchor="silk_independent_gain_lsb_pdf" 2214 title="PDF for Independent Quantization Gain LSB Coding"> 2215 <ttcol align="left">PDF</ttcol> 2216 <c>{32, 32, 32, 32, 32, 32, 32, 32}/256</c> 2217 </texttable> 2218 2219 <t> 2220 These 6 bits are combined to form a value, gain_index, between 0 and 63. 2221 When the gain for the previous subframe is available, then the current gain is 2222 limited as follows: 2223 <figure align="center"> 2224 <artwork align="center"><![CDATA[ 2225 log_gain = max(gain_index, previous_log_gain - 16) . 2226 ]]></artwork> 2227 </figure> 2228 This may help some implementations limit the change in precision of their 2229 internal LTP history. 2230 The indices which this clamp applies to cannot simply be removed from the 2231 codebook, because previous_log_gain will not be available after packet loss. 2232 The clamping is skipped after a decoder reset, and in the side channel if the 2233 previous frame in the side channel was not coded, since there is no value for 2234 previous_log_gain available. 2235 It MAY also be skipped after packet loss. 2236 </t> 2237 2238 <t> 2239 For subframes which do not have an independent gain (including the first 2240 subframe of frames not listed as using independent coding above), the 2241 quantization gain is coded relative to the gain from the previous subframe (in 2242 the same channel). 2243 The PDF in <xref target="silk_delta_gain_pdf"/> yields a delta_gain_index value 2244 between 0 and 40, inclusive. 2245 </t> 2246 <texttable anchor="silk_delta_gain_pdf" 2247 title="PDF for Delta Quantization Gain Coding"> 2248 <ttcol align="left">PDF</ttcol> 2249 <c>{6, 5, 11, 31, 132, 21, 8, 4, 2250 3, 2, 2, 2, 1, 1, 1, 1, 2251 1, 1, 1, 1, 1, 1, 1, 1, 2252 1, 1, 1, 1, 1, 1, 1, 1, 2253 1, 1, 1, 1, 1, 1, 1, 1, 1}/256</c> 2254 </texttable> 2255 <t> 2256 The following formula translates this index into a quantization gain for the 2257 current subframe using the gain from the previous subframe: 2258 <figure align="center"> 2259 <artwork align="center"><![CDATA[ 2260 log_gain = clamp(0, max(2*delta_gain_index - 16, 2261 previous_log_gain + delta_gain_index - 4), 63) . 2262 ]]></artwork> 2263 </figure> 2264 </t> 2265 <t> 2266 silk_gains_dequant() (gain_quant.c) dequantizes log_gain for the k'th subframe 2267 and converts it into a linear Q16 scale factor via 2268 <figure align="center"> 2269 <artwork align="center"><![CDATA[ 2270 gain_Q16[k] = silk_log2lin((0x1D1C71*log_gain>>16) + 2090) 2271 ]]></artwork> 2272 </figure> 2273 </t> 2274 <t> 2275 The function silk_log2lin() (log2lin.c) computes an approximation of 2276 2**(inLog_Q7/128.0), where inLog_Q7 is its Q7 input. 2277 Let i = inLog_Q7>>7 be the integer part of inLogQ7 and 2278 f = inLog_Q7&127 be the fractional part. 2279 Then 2280 <figure align="center"> 2281 <artwork align="center"><![CDATA[ 2282 (1<<i) + ((-174*f*(128-f)>>16)+f)*((1<<i)>>7) 2283 ]]></artwork> 2284 </figure> 2285 yields the approximate exponential. 2286 The final Q16 gain values lies between 81920 and 1686110208, inclusive 2287 (representing scale factors of 1.25 to 25728, respectively). 2288 </t> 2289 </section> 2290 2291 <section anchor="silk_nlsfs" toc="include" title="Normalized Line Spectral 2292 Frequency (LSF) and Linear Predictive Coding (LPC) Coefficients"> 2293 <t> 2294 A set of normalized Line Spectral Frequency (LSF) coefficients follow the 2295 quantization gains in the bitstream, and represent the Linear Predictive 2296 Coding (LPC) coefficients for the current SILK frame. 2297 Once decoded, the normalized LSFs form an increasing list of Q15 values between 2298 0 and 1. 2299 These represent the interleaved zeros on the upper half of the unit circle 2300 (between 0 and pi, hence "normalized") in the standard decomposition 2301 <xref target="line-spectral-pairs"/> of the LPC filter into a symmetric part 2302 and an anti-symmetric part (P and Q in <xref target="silk_nlsf2lpc"/>). 2303 Because of non-linear effects in the decoding process, an implementation SHOULD 2304 match the fixed-point arithmetic described in this section exactly. 2305 An encoder SHOULD also use the same process. 2306 </t> 2307 <t> 2308 The normalized LSFs are coded using a two-stage vector quantizer (VQ) 2309 (<xref target="silk_nlsf_stage1"/> and <xref target="silk_nlsf_stage2"/>). 2310 NB and MB frames use an order-10 predictor, while WB frames use an order-16 2311 predictor, and thus have different sets of tables. 2312 After reconstructing the normalized LSFs 2313 (<xref target="silk_nlsf_reconstruction"/>), the decoder runs them through a 2314 stabilization process (<xref target="silk_nlsf_stabilization"/>), interpolates 2315 them between frames (<xref target="silk_nlsf_interpolation"/>), converts them 2316 back into LPC coefficients (<xref target="silk_nlsf2lpc"/>), and then runs 2317 them through further processes to limit the range of the coefficients 2318 (<xref target="silk_lpc_range_limit"/>) and the gain of the filter 2319 (<xref target="silk_lpc_gain_limit"/>). 2320 All of this is necessary to ensure the reconstruction process is stable. 2321 </t> 2322 2323 <section anchor="silk_nlsf_stage1" title="Normalized LSF Stage 1 Decoding"> 2324 <t> 2325 The first VQ stage uses a 32-element codebook, coded with one of the PDFs in 2326 <xref target="silk_nlsf_stage1_pdfs"/>, depending on the audio bandwidth and 2327 the signal type of the current SILK frame. 2328 This yields a single index, I1, for the entire frame, which 2329 <list style="numbers"> 2330 <t>Indexes an element in a coarse codebook,</t> 2331 <t>Selects the PDFs for the second stage of the VQ, and</t> 2332 <t>Selects the prediction weights used to remove intra-frame redundancy from 2333 the second stage.</t> 2334 </list> 2335 The actual codebook elements are listed in 2336 <xref target="silk_nlsf_nbmb_codebook"/> and 2337 <xref target="silk_nlsf_wb_codebook"/>, but they are not needed until the last 2338 stages of reconstructing the LSF coefficients. 2339 </t> 2340 2341 <texttable anchor="silk_nlsf_stage1_pdfs" 2342 title="PDFs for Normalized LSF Stage-1 Index Decoding"> 2343 <ttcol align="left">Audio Bandwidth</ttcol> 2344 <ttcol align="left">Signal Type</ttcol> 2345 <ttcol align="left">PDF</ttcol> 2346 <c>NB or MB</c> <c>Inactive or unvoiced</c> 2347 <c> 2348 {44, 34, 30, 19, 21, 12, 11, 3, 2349 3, 2, 16, 2, 2, 1, 5, 2, 2350 1, 3, 3, 1, 1, 2, 2, 2, 2351 3, 1, 9, 9, 2, 7, 2, 1}/256 2352 </c> 2353 <c>NB or MB</c> <c>Voiced</c> 2354 <c> 2355 {1, 10, 1, 8, 3, 8, 8, 14, 2356 13, 14, 1, 14, 12, 13, 11, 11, 2357 12, 11, 10, 10, 11, 8, 9, 8, 2358 7, 8, 1, 1, 6, 1, 6, 5}/256 2359 </c> 2360 <c>WB</c> <c>Inactive or unvoiced</c> 2361 <c> 2362 {31, 21, 3, 17, 1, 8, 17, 4, 2363 1, 18, 16, 4, 2, 3, 1, 10, 2364 1, 3, 16, 11, 16, 2, 2, 3, 2365 2, 11, 1, 4, 9, 8, 7, 3}/256 2366 </c> 2367 <c>WB</c> <c>Voiced</c> 2368 <c> 2369 {1, 4, 16, 5, 18, 11, 5, 14, 2370 15, 1, 3, 12, 13, 14, 14, 6, 2371 14, 12, 2, 6, 1, 12, 12, 11, 2372 10, 3, 10, 5, 1, 1, 1, 3}/256 2373 </c> 2374 </texttable> 2375 2376 </section> 2377 2378 <section anchor="silk_nlsf_stage2" title="Normalized LSF Stage 2 Decoding"> 2379 <t> 2380 A total of 16 PDFs are available for the LSF residual in the second stage: the 2381 8 (a...h) for NB and MB frames given in 2382 <xref target="silk_nlsf_stage2_nbmb_pdfs"/>, and the 8 (i...p) for WB frames 2383 given in <xref target="silk_nlsf_stage2_wb_pdfs"/>. 2384 Which PDF is used for which coefficient is driven by the index, I1, 2385 decoded in the first stage. 2386 <xref target="silk_nlsf_nbmb_stage2_cb_sel"/> lists the letter of the 2387 corresponding PDF for each normalized LSF coefficient for NB and MB, and 2388 <xref target="silk_nlsf_wb_stage2_cb_sel"/> lists the same information for WB. 2389 </t> 2390 2391 <texttable anchor="silk_nlsf_stage2_nbmb_pdfs" 2392 title="PDFs for NB/MB Normalized LSF Stage-2 Index Decoding"> 2393 <ttcol align="left">Codebook</ttcol> 2394 <ttcol align="left">PDF</ttcol> 2395 <c>a</c> <c>{1, 1, 1, 15, 224, 11, 1, 1, 1}/256</c> 2396 <c>b</c> <c>{1, 1, 2, 34, 183, 32, 1, 1, 1}/256</c> 2397 <c>c</c> <c>{1, 1, 4, 42, 149, 55, 2, 1, 1}/256</c> 2398 <c>d</c> <c>{1, 1, 8, 52, 123, 61, 8, 1, 1}/256</c> 2399 <c>e</c> <c>{1, 3, 16, 53, 101, 74, 6, 1, 1}/256</c> 2400 <c>f</c> <c>{1, 3, 17, 55, 90, 73, 15, 1, 1}/256</c> 2401 <c>g</c> <c>{1, 7, 24, 53, 74, 67, 26, 3, 1}/256</c> 2402 <c>h</c> <c>{1, 1, 18, 63, 78, 58, 30, 6, 1}/256</c> 2403 </texttable> 2404 2405 <texttable anchor="silk_nlsf_stage2_wb_pdfs" 2406 title="PDFs for WB Normalized LSF Stage-2 Index Decoding"> 2407 <ttcol align="left">Codebook</ttcol> 2408 <ttcol align="left">PDF</ttcol> 2409 <c>i</c> <c>{1, 1, 1, 9, 232, 9, 1, 1, 1}/256</c> 2410 <c>j</c> <c>{1, 1, 2, 28, 186, 35, 1, 1, 1}/256</c> 2411 <c>k</c> <c>{1, 1, 3, 42, 152, 53, 2, 1, 1}/256</c> 2412 <c>l</c> <c>{1, 1, 10, 49, 126, 65, 2, 1, 1}/256</c> 2413 <c>m</c> <c>{1, 4, 19, 48, 100, 77, 5, 1, 1}/256</c> 2414 <c>n</c> <c>{1, 1, 14, 54, 100, 72, 12, 1, 1}/256</c> 2415 <c>o</c> <c>{1, 1, 15, 61, 87, 61, 25, 4, 1}/256</c> 2416 <c>p</c> <c>{1, 7, 21, 50, 77, 81, 17, 1, 1}/256</c> 2417 </texttable> 2418 2419 <texttable anchor="silk_nlsf_nbmb_stage2_cb_sel" 2420 title="Codebook Selection for NB/MB Normalized LSF Stage-2 Index Decoding"> 2421 <ttcol>I1</ttcol> 2422 <ttcol>Coefficient</ttcol> 2423 <c/> 2424 <c><spanx style="vbare">0 1 2 3 4 5 6 7 8 9</spanx></c> 2425 <c> 0</c> 2426 <c><spanx style="vbare">a a a a a a a a a a</spanx></c> 2427 <c> 1</c> 2428 <c><spanx style="vbare">b d b c c b c b b b</spanx></c> 2429 <c> 2</c> 2430 <c><spanx style="vbare">c b b b b b b b b b</spanx></c> 2431 <c> 3</c> 2432 <c><spanx style="vbare">b c c c c b c b b b</spanx></c> 2433 <c> 4</c> 2434 <c><spanx style="vbare">c d d d d c c c c c</spanx></c> 2435 <c> 5</c> 2436 <c><spanx style="vbare">a f d d c c c c b b</spanx></c> 2437 <c> g</c> 2438 <c><spanx style="vbare">a c c c c c c c c b</spanx></c> 2439 <c> 7</c> 2440 <c><spanx style="vbare">c d g e e e f e f f</spanx></c> 2441 <c> 8</c> 2442 <c><spanx style="vbare">c e f f e f e g e e</spanx></c> 2443 <c> 9</c> 2444 <c><spanx style="vbare">c e e h e f e f f e</spanx></c> 2445 <c>10</c> 2446 <c><spanx style="vbare">e d d d c d c c c c</spanx></c> 2447 <c>11</c> 2448 <c><spanx style="vbare">b f f g e f e f f f</spanx></c> 2449 <c>12</c> 2450 <c><spanx style="vbare">c h e g f f f f f f</spanx></c> 2451 <c>13</c> 2452 <c><spanx style="vbare">c h f f f f f g f e</spanx></c> 2453 <c>14</c> 2454 <c><spanx style="vbare">d d f e e f e f e e</spanx></c> 2455 <c>15</c> 2456 <c><spanx style="vbare">c d d f f e e e e e</spanx></c> 2457 <c>16</c> 2458 <c><spanx style="vbare">c e e g e f e f f f</spanx></c> 2459 <c>17</c> 2460 <c><spanx style="vbare">c f e g f f f e f e</spanx></c> 2461 <c>18</c> 2462 <c><spanx style="vbare">c h e f e f e f f f</spanx></c> 2463 <c>19</c> 2464 <c><spanx style="vbare">c f e g h g f g f e</spanx></c> 2465 <c>20</c> 2466 <c><spanx style="vbare">d g h e g f f g e f</spanx></c> 2467 <c>21</c> 2468 <c><spanx style="vbare">c h g e e e f e f f</spanx></c> 2469 <c>22</c> 2470 <c><spanx style="vbare">e f f e g g f g f e</spanx></c> 2471 <c>23</c> 2472 <c><spanx style="vbare">c f f g f g e g e e</spanx></c> 2473 <c>24</c> 2474 <c><spanx style="vbare">e f f f d h e f f e</spanx></c> 2475 <c>25</c> 2476 <c><spanx style="vbare">c d e f f g e f f e</spanx></c> 2477 <c>26</c> 2478 <c><spanx style="vbare">c d c d d e c d d d</spanx></c> 2479 <c>27</c> 2480 <c><spanx style="vbare">b b c c c c c d c c</spanx></c> 2481 <c>28</c> 2482 <c><spanx style="vbare">e f f g g g f g e f</spanx></c> 2483 <c>29</c> 2484 <c><spanx style="vbare">d f f e e e e d d c</spanx></c> 2485 <c>30</c> 2486 <c><spanx style="vbare">c f d h f f e e f e</spanx></c> 2487 <c>31</c> 2488 <c><spanx style="vbare">e e f e f g f g f e</spanx></c> 2489 </texttable> 2490 2491 <texttable anchor="silk_nlsf_wb_stage2_cb_sel" 2492 title="Codebook Selection for WB Normalized LSF Stage-2 Index Decoding"> 2493 <ttcol>I1</ttcol> 2494 <ttcol>Coefficient</ttcol> 2495 <c/> 2496 <c><spanx style="vbare">0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15</spanx></c> 2497 <c> 0</c> 2498 <c><spanx style="vbare">i i i i i i i i i i i i i i i i</spanx></c> 2499 <c> 1</c> 2500 <c><spanx style="vbare">k l l l l l k k k k k j j j i l</spanx></c> 2501 <c> 2</c> 2502 <c><spanx style="vbare">k n n l p m m n k n m n n m l l</spanx></c> 2503 <c> 3</c> 2504 <c><spanx style="vbare">i k j k k j j j j j i i i i i j</spanx></c> 2505 <c> 4</c> 2506 <c><spanx style="vbare">i o n m o m p n m m m n n m m l</spanx></c> 2507 <c> 5</c> 2508 <c><spanx style="vbare">i l n n m l l n l l l l l l k m</spanx></c> 2509 <c> 6</c> 2510 <c><spanx style="vbare">i i i i i i i i i i i i i i i i</spanx></c> 2511 <c> 7</c> 2512 <c><spanx style="vbare">i k o l p k n l m n n m l l k l</spanx></c> 2513 <c> 8</c> 2514 <c><spanx style="vbare">i o k o o m n m o n m m n l l l</spanx></c> 2515 <c> 9</c> 2516 <c><spanx style="vbare">k j i i i i i i i i i i i i i i</spanx></c> 2517 <c>10</c> 2518 <c><spanx style="vbare">i j i i i i i i i i i i i i i j</spanx></c> 2519 <c>11</c> 2520 <c><spanx style="vbare">k k l m n l l l l l l l k k j l</spanx></c> 2521 <c>12</c> 2522 <c><spanx style="vbare">k k l l m l l l l l l l l k j l</spanx></c> 2523 <c>13</c> 2524 <c><spanx style="vbare">l m m m o m m n l n m m n m l m</spanx></c> 2525 <c>14</c> 2526 <c><spanx style="vbare">i o m n m p n k o n p m m l n l</spanx></c> 2527 <c>15</c> 2528 <c><spanx style="vbare">i j i j j j j j j j i i i i j i</spanx></c> 2529 <c>16</c> 2530 <c><spanx style="vbare">j o n p n m n l m n m m m l l m</spanx></c> 2531 <c>17</c> 2532 <c><spanx style="vbare">j l l m m l l n k l l n n n l m</spanx></c> 2533 <c>18</c> 2534 <c><spanx style="vbare">k l l k k k l k j k j k j j j m</spanx></c> 2535 <c>19</c> 2536 <c><spanx style="vbare">i k l n l l k k k j j i i i i i</spanx></c> 2537 <c>20</c> 2538 <c><spanx style="vbare">l m l n l l k k j j j j j k k m</spanx></c> 2539 <c>21</c> 2540 <c><spanx style="vbare">k o l p p m n m n l n l l k l l</spanx></c> 2541 <c>22</c> 2542 <c><spanx style="vbare">k l n o o l n l m m l l l l k m</spanx></c> 2543 <c>23</c> 2544 <c><spanx style="vbare">j l l m m m m l n n n l j j j j</spanx></c> 2545 <c>24</c> 2546 <c><spanx style="vbare">k n l o o m p m m n l m m l l l</spanx></c> 2547 <c>25</c> 2548 <c><spanx style="vbare">i o j j i i i i i i i i i i i i</spanx></c> 2549 <c>26</c> 2550 <c><spanx style="vbare">i o o l n k n n l m m p p m m m</spanx></c> 2551 <c>27</c> 2552 <c><spanx style="vbare">l l p l n m l l l k k l l l k l</spanx></c> 2553 <c>28</c> 2554 <c><spanx style="vbare">i i j i i i k j k j j k k k j j</spanx></c> 2555 <c>29</c> 2556 <c><spanx style="vbare">i l k n l l k l k j i i j i i j</spanx></c> 2557 <c>30</c> 2558 <c><spanx style="vbare">l n n m p n l l k l k k j i j i</spanx></c> 2559 <c>31</c> 2560 <c><spanx style="vbare">k l n l m l l l k j k o m i i i</spanx></c> 2561 </texttable> 2562 2563 <t> 2564 Decoding the second stage residual proceeds as follows. 2565 For each coefficient, the decoder reads a symbol using the PDF corresponding to 2566 I1 from either <xref target="silk_nlsf_nbmb_stage2_cb_sel"/> or 2567 <xref target="silk_nlsf_wb_stage2_cb_sel"/>, and subtracts 4 from the result 2568 to give an index in the range -4 to 4, inclusive. 2569 If the index is either -4 or 4, it reads a second symbol using the PDF in 2570 <xref target="silk_nlsf_ext_pdf"/>, and adds the value of this second symbol 2571 to the index, using the same sign. 2572 This gives the index, I2[k], a total range of -10 to 10, inclusive. 2573 </t> 2574 2575 <texttable anchor="silk_nlsf_ext_pdf" 2576 title="PDF for Normalized LSF Index Extension Decoding"> 2577 <ttcol align="left">PDF</ttcol> 2578 <c>{156, 60, 24, 9, 4, 2, 1}/256</c> 2579 </texttable> 2580 2581 <t> 2582 The decoded indices from both stages are translated back into normalized LSF 2583 coefficients in silk_NLSF_decode() (NLSF_decode.c). 2584 The stage-2 indices represent residuals after both the first stage of the VQ 2585 and a separate backwards-prediction step. 2586 The backwards prediction process in the encoder subtracts a prediction from 2587 each residual formed by a multiple of the coefficient that follows it. 2588 The decoder must undo this process. 2589 <xref target="silk_nlsf_pred_weights"/> contains lists of prediction weights 2590 for each coefficient. 2591 There are two lists for NB and MB, and another two lists for WB, giving two 2592 possible prediction weights for each coefficient. 2593 </t> 2594 2595 <texttable anchor="silk_nlsf_pred_weights" 2596 title="Prediction Weights for Normalized LSF Decoding"> 2597 <ttcol align="left">Coefficient</ttcol> 2598 <ttcol align="right">A</ttcol> 2599 <ttcol align="right">B</ttcol> 2600 <ttcol align="right">C</ttcol> 2601 <ttcol align="right">D</ttcol> 2602 <c>0</c> <c>179</c> <c>116</c> <c>175</c> <c>68</c> 2603 <c>1</c> <c>138</c> <c>67</c> <c>148</c> <c>62</c> 2604 <c>2</c> <c>140</c> <c>82</c> <c>160</c> <c>66</c> 2605 <c>3</c> <c>148</c> <c>59</c> <c>176</c> <c>60</c> 2606 <c>4</c> <c>151</c> <c>92</c> <c>178</c> <c>72</c> 2607 <c>5</c> <c>149</c> <c>72</c> <c>173</c> <c>117</c> 2608 <c>6</c> <c>153</c> <c>100</c> <c>174</c> <c>85</c> 2609 <c>7</c> <c>151</c> <c>89</c> <c>164</c> <c>90</c> 2610 <c>8</c> <c>163</c> <c>92</c> <c>177</c> <c>118</c> 2611 <c>9</c> <c/> <c/> <c>174</c> <c>136</c> 2612 <c>10</c> <c/> <c/> <c>196</c> <c>151</c> 2613 <c>11</c> <c/> <c/> <c>182</c> <c>142</c> 2614 <c>12</c> <c/> <c/> <c>198</c> <c>160</c> 2615 <c>13</c> <c/> <c/> <c>192</c> <c>142</c> 2616 <c>14</c> <c/> <c/> <c>182</c> <c>155</c> 2617 </texttable> 2618 2619 <t> 2620 The prediction is undone using the procedure implemented in 2621 silk_NLSF_residual_dequant() (NLSF_decode.c), which is as follows. 2622 Each coefficient selects its prediction weight from one of the two lists based 2623 on the stage-1 index, I1. 2624 <xref target="silk_nlsf_nbmb_weight_sel"/> gives the selections for each 2625 coefficient for NB and MB, and <xref target="silk_nlsf_wb_weight_sel"/> gives 2626 the selections for WB. 2627 Let d_LPC be the order of the codebook, i.e., 10 for NB and MB, and 16 for WB, 2628 and let pred_Q8[k] be the weight for the k'th coefficient selected by this 2629 process for 0 <= k < d_LPC-1. 2630 Then, the stage-2 residual for each coefficient is computed via 2631 <figure align="center"> 2632 <artwork align="center"><![CDATA[ 2633 res_Q10[k] = (k+1 < d_LPC ? (res_Q10[k+1]*pred_Q8[k])>>8 : 0) 2634 + ((((I2[k]<<10) - sign(I2[k])*102)*qstep)>>16) , 2635 ]]></artwork> 2636 </figure> 2637 where qstep is the Q16 quantization step size, which is 11796 for NB and MB 2638 and 9830 for WB (representing step sizes of approximately 0.18 and 0.15, 2639 respectively). 2640 </t> 2641 2642 <texttable anchor="silk_nlsf_nbmb_weight_sel" 2643 title="Prediction Weight Selection for NB/MB Normalized LSF Decoding"> 2644 <ttcol>I1</ttcol> 2645 <ttcol>Coefficient</ttcol> 2646 <c/> 2647 <c><spanx style="vbare">0 1 2 3 4 5 6 7 8</spanx></c> 2648 <c> 0</c> 2649 <c><spanx style="vbare">A B A A A A A A A</spanx></c> 2650 <c> 1</c> 2651 <c><spanx style="vbare">B A A A A A A A A</spanx></c> 2652 <c> 2</c> 2653 <c><spanx style="vbare">A A A A A A A A A</spanx></c> 2654 <c> 3</c> 2655 <c><spanx style="vbare">B B B A A A A B A</spanx></c> 2656 <c> 4</c> 2657 <c><spanx style="vbare">A B A A A A A A A</spanx></c> 2658 <c> 5</c> 2659 <c><spanx style="vbare">A B A A A A A A A</spanx></c> 2660 <c> 6</c> 2661 <c><spanx style="vbare">B A B B A A A B A</spanx></c> 2662 <c> 7</c> 2663 <c><spanx style="vbare">A B B A A B B A A</spanx></c> 2664 <c> 8</c> 2665 <c><spanx style="vbare">A A B B A B A B B</spanx></c> 2666 <c> 9</c> 2667 <c><spanx style="vbare">A A B B A A B B B</spanx></c> 2668 <c>10</c> 2669 <c><spanx style="vbare">A A A A A A A A A</spanx></c> 2670 <c>11</c> 2671 <c><spanx style="vbare">A B A B B B B B A</spanx></c> 2672 <c>12</c> 2673 <c><spanx style="vbare">A B A B B B B B A</spanx></c> 2674 <c>13</c> 2675 <c><spanx style="vbare">A B B B B B B B A</spanx></c> 2676 <c>14</c> 2677 <c><spanx style="vbare">B A B B A B B B B</spanx></c> 2678 <c>15</c> 2679 <c><spanx style="vbare">A B B B B B A B A</spanx></c> 2680 <c>16</c> 2681 <c><spanx style="vbare">A A B B A B A B A</spanx></c> 2682 <c>17</c> 2683 <c><spanx style="vbare">A A B B B A B B B</spanx></c> 2684 <c>18</c> 2685 <c><spanx style="vbare">A B B A A B B B A</spanx></c> 2686 <c>19</c> 2687 <c><spanx style="vbare">A A A B B B A B A</spanx></c> 2688 <c>20</c> 2689 <c><spanx style="vbare">A B B A A B A B A</spanx></c> 2690 <c>21</c> 2691 <c><spanx style="vbare">A B B A A A B B A</spanx></c> 2692 <c>22</c> 2693 <c><spanx style="vbare">A A A A A B B B B</spanx></c> 2694 <c>23</c> 2695 <c><spanx style="vbare">A A B B A A A B B</spanx></c> 2696 <c>24</c> 2697 <c><spanx style="vbare">A A A B A B B B B</spanx></c> 2698 <c>25</c> 2699 <c><spanx style="vbare">A B B B B B B B A</spanx></c> 2700 <c>26</c> 2701 <c><spanx style="vbare">A A A A A A A A A</spanx></c> 2702 <c>27</c> 2703 <c><spanx style="vbare">A A A A A A A A A</spanx></c> 2704 <c>28</c> 2705 <c><spanx style="vbare">A A B A B B A B A</spanx></c> 2706 <c>29</c> 2707 <c><spanx style="vbare">B A A B A A A A A</spanx></c> 2708 <c>30</c> 2709 <c><spanx style="vbare">A A A B B A B A B</spanx></c> 2710 <c>31</c> 2711 <c><spanx style="vbare">B A B B A B B B B</spanx></c> 2712 </texttable> 2713 2714 <texttable anchor="silk_nlsf_wb_weight_sel" 2715 title="Prediction Weight Selection for WB Normalized LSF Decoding"> 2716 <ttcol>I1</ttcol> 2717 <ttcol>Coefficient</ttcol> 2718 <c/> 2719 <c><spanx style="vbare">0 1 2 3 4 5 6 7 8 9 10 11 12 13 14</spanx></c> 2720 <c> 0</c> 2721 <c><spanx style="vbare">C C C C C C C C C C C C C C D</spanx></c> 2722 <c> 1</c> 2723 <c><spanx style="vbare">C C C C C C C C C C C C C C C</spanx></c> 2724 <c> 2</c> 2725 <c><spanx style="vbare">C C D C C D D D C D D D D C C</spanx></c> 2726 <c> 3</c> 2727 <c><spanx style="vbare">C C C C C C C C C C C C D C C</spanx></c> 2728 <c> 4</c> 2729 <c><spanx style="vbare">C D D C D C D D C D D D D D C</spanx></c> 2730 <c> 5</c> 2731 <c><spanx style="vbare">C C D C C C C C C C C C C C C</spanx></c> 2732 <c> 6</c> 2733 <c><spanx style="vbare">D C C C C C C C C C C D C D C</spanx></c> 2734 <c> 7</c> 2735 <c><spanx style="vbare">C D D C C C D C D D D C D C D</spanx></c> 2736 <c> 8</c> 2737 <c><spanx style="vbare">C D C D D C D C D C D D D D D</spanx></c> 2738 <c> 9</c> 2739 <c><spanx style="vbare">C C C C C C C C C C C C C C D</spanx></c> 2740 <c>10</c> 2741 <c><spanx style="vbare">C D C C C C C C C C C C C C C</spanx></c> 2742 <c>11</c> 2743 <c><spanx style="vbare">C C D C D D D D D D D C D C C</spanx></c> 2744 <c>12</c> 2745 <c><spanx style="vbare">C C D C C D C D C D C C D C C</spanx></c> 2746 <c>13</c> 2747 <c><spanx style="vbare">C C C C D D C D C D D D D C C</spanx></c> 2748 <c>14</c> 2749 <c><spanx style="vbare">C D C C C D D C D D D C D D D</spanx></c> 2750 <c>15</c> 2751 <c><spanx style="vbare">C C D D C C C C C C C C D D C</spanx></c> 2752 <c>16</c> 2753 <c><spanx style="vbare">C D D C D C D D D D D C D C C</spanx></c> 2754 <c>17</c> 2755 <c><spanx style="vbare">C C D C C C C D C C D D D C C</spanx></c> 2756 <c>18</c> 2757 <c><spanx style="vbare">C C C C C C C C C C C C C C D</spanx></c> 2758 <c>19</c> 2759 <c><spanx style="vbare">C C C C C C C C C C C C D C C</spanx></c> 2760 <c>20</c> 2761 <c><spanx style="vbare">C C C C C C C C C C C C C C C</spanx></c> 2762 <c>21</c> 2763 <c><spanx style="vbare">C D C D C D D C D C D C D D C</spanx></c> 2764 <c>22</c> 2765 <c><spanx style="vbare">C C D D D D C D D C C D D C C</spanx></c> 2766 <c>23</c> 2767 <c><spanx style="vbare">C D D C D C D C D C C C C D C</spanx></c> 2768 <c>24</c> 2769 <c><spanx style="vbare">C C C D D C D C D D D D D D D</spanx></c> 2770 <c>25</c> 2771 <c><spanx style="vbare">C C C C C C C C C C C C C C D</spanx></c> 2772 <c>26</c> 2773 <c><spanx style="vbare">C D D C C C D D C C D D D D D</spanx></c> 2774 <c>27</c> 2775 <c><spanx style="vbare">C C C C C D C D D D D C D D D</spanx></c> 2776 <c>28</c> 2777 <c><spanx style="vbare">C C C C C C C C C C C C C C D</spanx></c> 2778 <c>29</c> 2779 <c><spanx style="vbare">C C C C C C C C C C C C C C D</spanx></c> 2780 <c>30</c> 2781 <c><spanx style="vbare">D C C C C C C C C C C D C C C</spanx></c> 2782 <c>31</c> 2783 <c><spanx style="vbare">C C D C C D D D C C D C C D C</spanx></c> 2784 </texttable> 2785 2786 </section> 2787 2788 <section anchor="silk_nlsf_reconstruction" 2789 title="Reconstructing the Normalized LSF Coefficients"> 2790 <t> 2791 Once the stage-1 index I1 and the stage-2 residual res_Q10[] have been decoded, 2792 the final normalized LSF coefficients can be reconstructed. 2793 </t> 2794 <t> 2795 The spectral distortion introduced by the quantization of each LSF coefficient 2796 varies, so the stage-2 residual is weighted accordingly, using the 2797 low-complexity Inverse Harmonic Mean Weighting (IHMW) function proposed in 2798 <xref target="laroia-icassp"/>. 2799 The weights are derived directly from the stage-1 codebook vector. 2800 Let cb1_Q8[k] be the k'th entry of the stage-1 codebook vector from 2801 <xref target="silk_nlsf_nbmb_codebook"/> or 2802 <xref target="silk_nlsf_wb_codebook"/>. 2803 Then for 0 <= k < d_LPC the following expression 2804 computes the square of the weight as a Q18 value: 2805 <figure align="center"> 2806 <artwork align="center"> 2807 <![CDATA[ 2808 w2_Q18[k] = (1024/(cb1_Q8[k] - cb1_Q8[k-1]) 2809 + 1024/(cb1_Q8[k+1] - cb1_Q8[k])) << 16 , 2810 ]]> 2811 </artwork> 2812 </figure> 2813 where cb1_Q8[-1] = 0 and cb1_Q8[d_LPC] = 256, and the 2814 division is integer division. 2815 This is reduced to an unsquared, Q9 value using the following square-root 2816 approximation: 2817 <figure align="center"> 2818 <artwork align="center"><![CDATA[ 2819 i = ilog(w2_Q18[k]) 2820 f = (w2_Q18[k]>>(i-8)) & 127 2821 y = ((i&1) ? 32768 : 46214) >> ((32-i)>>1) 2822 w_Q9[k] = y + ((213*f*y)>>16) 2823 ]]></artwork> 2824 </figure> 2825 The constant 46214 here is approximately the square root of 2 in Q15. 2826 The cb1_Q8[] vector completely determines these weights, and they may be 2827 tabulated and stored as 13-bit unsigned values (with a range of 1819 to 5227, 2828 inclusive) to avoid computing them when decoding. 2829 The reference implementation already requires code to compute these weights on 2830 unquantized coefficients in the encoder, in silk_NLSF_VQ_weights_laroia() 2831 (NLSF_VQ_weights_laroia.c) and its callers, so it reuses that code in the 2832 decoder instead of using a pre-computed table to reduce the amount of ROM 2833 required. 2834 </t> 2835 2836 <texttable anchor="silk_nlsf_nbmb_codebook" 2837 title="NB/MB Normalized LSF Stage-1 Codebook Vectors"> 2838 <ttcol>I1</ttcol> 2839 <ttcol>Codebook (Q8)</ttcol> 2840 <c/> 2841 <c><spanx style="vbare"> 0 1 2 3 4 5 6 7 8 9</spanx></c> 2842 <c>0</c> 2843 <c><spanx style="vbare">12 35 60 83 108 132 157 180 206 228</spanx></c> 2844 <c>1</c> 2845 <c><spanx style="vbare">15 32 55 77 101 125 151 175 201 225</spanx></c> 2846 <c>2</c> 2847 <c><spanx style="vbare">19 42 66 89 114 137 162 184 209 230</spanx></c> 2848 <c>3</c> 2849 <c><spanx style="vbare">12 25 50 72 97 120 147 172 200 223</spanx></c> 2850 <c>4</c> 2851 <c><spanx style="vbare">26 44 69 90 114 135 159 180 205 225</spanx></c> 2852 <c>5</c> 2853 <c><spanx style="vbare">13 22 53 80 106 130 156 180 205 228</spanx></c> 2854 <c>6</c> 2855 <c><spanx style="vbare">15 25 44 64 90 115 142 168 196 222</spanx></c> 2856 <c>7</c> 2857 <c><spanx style="vbare">19 24 62 82 100 120 145 168 190 214</spanx></c> 2858 <c>8</c> 2859 <c><spanx style="vbare">22 31 50 79 103 120 151 170 203 227</spanx></c> 2860 <c>9</c> 2861 <c><spanx style="vbare">21 29 45 65 106 124 150 171 196 224</spanx></c> 2862 <c>10</c> 2863 <c><spanx style="vbare">30 49 75 97 121 142 165 186 209 229</spanx></c> 2864 <c>11</c> 2865 <c><spanx style="vbare">19 25 52 70 93 116 143 166 192 219</spanx></c> 2866 <c>12</c> 2867 <c><spanx style="vbare">26 34 62 75 97 118 145 167 194 217</spanx></c> 2868 <c>13</c> 2869 <c><spanx style="vbare">25 33 56 70 91 113 143 165 196 223</spanx></c> 2870 <c>14</c> 2871 <c><spanx style="vbare">21 34 51 72 97 117 145 171 196 222</spanx></c> 2872 <c>15</c> 2873 <c><spanx style="vbare">20 29 50 67 90 117 144 168 197 221</spanx></c> 2874 <c>16</c> 2875 <c><spanx style="vbare">22 31 48 66 95 117 146 168 196 222</spanx></c> 2876 <c>17</c> 2877 <c><spanx style="vbare">24 33 51 77 116 134 158 180 200 224</spanx></c> 2878 <c>18</c> 2879 <c><spanx style="vbare">21 28 70 87 106 124 149 170 194 217</spanx></c> 2880 <c>19</c> 2881 <c><spanx style="vbare">26 33 53 64 83 117 152 173 204 225</spanx></c> 2882 <c>20</c> 2883 <c><spanx style="vbare">27 34 65 95 108 129 155 174 210 225</spanx></c> 2884 <c>21</c> 2885 <c><spanx style="vbare">20 26 72 99 113 131 154 176 200 219</spanx></c> 2886 <c>22</c> 2887 <c><spanx style="vbare">34 43 61 78 93 114 155 177 205 229</spanx></c> 2888 <c>23</c> 2889 <c><spanx style="vbare">23 29 54 97 124 138 163 179 209 229</spanx></c> 2890 <c>24</c> 2891 <c><spanx style="vbare">30 38 56 89 118 129 158 178 200 231</spanx></c> 2892 <c>25</c> 2893 <c><spanx style="vbare">21 29 49 63 85 111 142 163 193 222</spanx></c> 2894 <c>26</c> 2895 <c><spanx style="vbare">27 48 77 103 133 158 179 196 215 232</spanx></c> 2896 <c>27</c> 2897 <c><spanx style="vbare">29 47 74 99 124 151 176 198 220 237</spanx></c> 2898 <c>28</c> 2899 <c><spanx style="vbare">33 42 61 76 93 121 155 174 207 225</spanx></c> 2900 <c>29</c> 2901 <c><spanx style="vbare">29 53 87 112 136 154 170 188 208 227</spanx></c> 2902 <c>30</c> 2903 <c><spanx style="vbare">24 30 52 84 131 150 166 186 203 229</spanx></c> 2904 <c>31</c> 2905 <c><spanx style="vbare">37 48 64 84 104 118 156 177 201 230</spanx></c> 2906 </texttable> 2907 2908 <texttable anchor="silk_nlsf_wb_codebook" 2909 title="WB Normalized LSF Stage-1 Codebook Vectors"> 2910 <ttcol>I1</ttcol> 2911 <ttcol>Codebook (Q8)</ttcol> 2912 <c/> 2913 <c><spanx style="vbare"> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15</spanx></c> 2914 <c>0</c> 2915 <c><spanx style="vbare"> 7 23 38 54 69 85 100 116 131 147 162 178 193 208 223 239</spanx></c> 2916 <c>1</c> 2917 <c><spanx style="vbare">13 25 41 55 69 83 98 112 127 142 157 171 187 203 220 236</spanx></c> 2918 <c>2</c> 2919 <c><spanx style="vbare">15 21 34 51 61 78 92 106 126 136 152 167 185 205 225 240</spanx></c> 2920 <c>3</c> 2921 <c><spanx style="vbare">10 21 36 50 63 79 95 110 126 141 157 173 189 205 221 237</spanx></c> 2922 <c>4</c> 2923 <c><spanx style="vbare">17 20 37 51 59 78 89 107 123 134 150 164 184 205 224 240</spanx></c> 2924 <c>5</c> 2925 <c><spanx style="vbare">10 15 32 51 67 81 96 112 129 142 158 173 189 204 220 236</spanx></c> 2926 <c>6</c> 2927 <c><spanx style="vbare"> 8 21 37 51 65 79 98 113 126 138 155 168 179 192 209 218</spanx></c> 2928 <c>7</c> 2929 <c><spanx style="vbare">12 15 34 55 63 78 87 108 118 131 148 167 185 203 219 236</spanx></c> 2930 <c>8</c> 2931 <c><spanx style="vbare">16 19 32 36 56 79 91 108 118 136 154 171 186 204 220 237</spanx></c> 2932 <c>9</c> 2933 <c><spanx style="vbare">11 28 43 58 74 89 105 120 135 150 165 180 196 211 226 241</spanx></c> 2934 <c>10</c> 2935 <c><spanx style="vbare"> 6 16 33 46 60 75 92 107 123 137 156 169 185 199 214 225</spanx></c> 2936 <c>11</c> 2937 <c><spanx style="vbare">11 19 30 44 57 74 89 105 121 135 152 169 186 202 218 234</spanx></c> 2938 <c>12</c> 2939 <c><spanx style="vbare">12 19 29 46 57 71 88 100 120 132 148 165 182 199 216 233</spanx></c> 2940 <c>13</c> 2941 <c><spanx style="vbare">17 23 35 46 56 77 92 106 123 134 152 167 185 204 222 237</spanx></c> 2942 <c>14</c> 2943 <c><spanx style="vbare">14 17 45 53 63 75 89 107 115 132 151 171 188 206 221 240</spanx></c> 2944 <c>15</c> 2945 <c><spanx style="vbare"> 9 16 29 40 56 71 88 103 119 137 154 171 189 205 222 237</spanx></c> 2946 <c>16</c> 2947 <c><spanx style="vbare">16 19 36 48 57 76 87 105 118 132 150 167 185 202 218 236</spanx></c> 2948 <c>17</c> 2949 <c><spanx style="vbare">12 17 29 54 71 81 94 104 126 136 149 164 182 201 221 237</spanx></c> 2950 <c>18</c> 2951 <c><spanx style="vbare">15 28 47 62 79 97 115 129 142 155 168 180 194 208 223 238</spanx></c> 2952 <c>19</c> 2953 <c><spanx style="vbare"> 8 14 30 45 62 78 94 111 127 143 159 175 192 207 223 239</spanx></c> 2954 <c>20</c> 2955 <c><spanx style="vbare">17 30 49 62 79 92 107 119 132 145 160 174 190 204 220 235</spanx></c> 2956 <c>21</c> 2957 <c><spanx style="vbare">14 19 36 45 61 76 91 108 121 138 154 172 189 205 222 238</spanx></c> 2958 <c>22</c> 2959 <c><spanx style="vbare">12 18 31 45 60 76 91 107 123 138 154 171 187 204 221 236</spanx></c> 2960 <c>23</c> 2961 <c><spanx style="vbare">13 17 31 43 53 70 83 103 114 131 149 167 185 203 220 237</spanx></c> 2962 <c>24</c> 2963 <c><spanx style="vbare">17 22 35 42 58 78 93 110 125 139 155 170 188 206 224 240</spanx></c> 2964 <c>25</c> 2965 <c><spanx style="vbare"> 8 15 34 50 67 83 99 115 131 146 162 178 193 209 224 239</spanx></c> 2966 <c>26</c> 2967 <c><spanx style="vbare">13 16 41 66 73 86 95 111 128 137 150 163 183 206 225 241</spanx></c> 2968 <c>27</c> 2969 <c><spanx style="vbare">17 25 37 52 63 75 92 102 119 132 144 160 175 191 212 231</spanx></c> 2970 <c>28</c> 2971 <c><spanx style="vbare">19 31 49 65 83 100 117 133 147 161 174 187 200 213 227 242</spanx></c> 2972 <c>29</c> 2973 <c><spanx style="vbare">18 31 52 68 88 103 117 126 138 149 163 177 192 207 223 239</spanx></c> 2974 <c>30</c> 2975 <c><spanx style="vbare">16 29 47 61 76 90 106 119 133 147 161 176 193 209 224 240</spanx></c> 2976 <c>31</c> 2977 <c><spanx style="vbare">15 21 35 50 61 73 86 97 110 119 129 141 175 198 218 237</spanx></c> 2978 </texttable> 2979 2980 <t> 2981 Given the stage-1 codebook entry cb1_Q8[], the stage-2 residual res_Q10[], and 2982 their corresponding weights, w_Q9[], the reconstructed normalized LSF 2983 coefficients are 2984 <figure align="center"> 2985 <artwork align="center"><![CDATA[ 2986 NLSF_Q15[k] = clamp(0, 2987 (cb1_Q8[k]<<7) + (res_Q10[k]<<14)/w_Q9[k], 32767) , 2988 ]]></artwork> 2989 </figure> 2990 where the division is integer division. 2991 However, nothing in either the reconstruction process or the 2992 quantization process in the encoder thus far guarantees that the coefficients 2993 are monotonically increasing and separated well enough to ensure a stable 2994 filter <xref target="Kabal86"/>. 2995 When using the reference encoder, roughly 2% of frames violate this constraint. 2996 The next section describes a stabilization procedure used to make these 2997 guarantees. 2998 </t> 2999 3000 </section> 3001 3002 <section anchor="silk_nlsf_stabilization" title="Normalized LSF Stabilization"> 3003 <t> 3004 The normalized LSF stabilization procedure is implemented in 3005 silk_NLSF_stabilize() (NLSF_stabilize.c). 3006 This process ensures that consecutive values of the normalized LSF 3007 coefficients, NLSF_Q15[], are spaced some minimum distance apart 3008 (predetermined to be the 0.01 percentile of a large training set). 3009 <xref target="silk_nlsf_min_spacing"/> gives the minimum spacings for NB and MB 3010 and those for WB, where row k is the minimum allowed value of 3011 NLSF_Q[k]-NLSF_Q[k-1]. 3012 For the purposes of computing this spacing for the first and last coefficient, 3013 NLSF_Q15[-1] is taken to be 0, and NLSF_Q15[d_LPC] is taken to be 32768. 3014 </t> 3015 3016 <texttable anchor="silk_nlsf_min_spacing" 3017 title="Minimum Spacing for Normalized LSF Coefficients"> 3018 <ttcol>Coefficient</ttcol> 3019 <ttcol align="right">NB and MB</ttcol> 3020 <ttcol align="right">WB</ttcol> 3021 <c>0</c> <c>250</c> <c>100</c> 3022 <c>1</c> <c>3</c> <c>3</c> 3023 <c>2</c> <c>6</c> <c>40</c> 3024 <c>3</c> <c>3</c> <c>3</c> 3025 <c>4</c> <c>3</c> <c>3</c> 3026 <c>5</c> <c>3</c> <c>3</c> 3027 <c>6</c> <c>4</c> <c>5</c> 3028 <c>7</c> <c>3</c> <c>14</c> 3029 <c>8</c> <c>3</c> <c>14</c> 3030 <c>9</c> <c>3</c> <c>10</c> 3031 <c>10</c> <c>461</c> <c>11</c> 3032 <c>11</c> <c/> <c>3</c> 3033 <c>12</c> <c/> <c>8</c> 3034 <c>13</c> <c/> <c>9</c> 3035 <c>14</c> <c/> <c>7</c> 3036 <c>15</c> <c/> <c>3</c> 3037 <c>16</c> <c/> <c>347</c> 3038 </texttable> 3039 3040 <t> 3041 The procedure starts off by trying to make small adjustments which attempt to 3042 minimize the amount of distortion introduced. 3043 After 20 such adjustments, it falls back to a more direct method which 3044 guarantees the constraints are enforced but may require large adjustments. 3045 </t> 3046 <t> 3047 Let NDeltaMin_Q15[k] be the minimum required spacing for the current audio 3048 bandwidth from <xref target="silk_nlsf_min_spacing"/>. 3049 First, the procedure finds the index i where 3050 NLSF_Q15[i] - NLSF_Q15[i-1] - NDeltaMin_Q15[i] is the 3051 smallest, breaking ties by using the lower value of i. 3052 If this value is non-negative, then the stabilization stops; the coefficients 3053 satisfy all the constraints. 3054 Otherwise, if i == 0, it sets NLSF_Q15[0] to NDeltaMin_Q15[0], and if 3055 i == d_LPC, it sets NLSF_Q15[d_LPC-1] to 3056 (32768 - NDeltaMin_Q15[d_LPC]). 3057 For all other values of i, both NLSF_Q15[i-1] and NLSF_Q15[i] are updated as 3058 follows: 3059 <figure align="center"> 3060 <artwork align="center"><![CDATA[ 3061 i-1 3062 __ 3063 min_center_Q15 = (NDeltaMin_Q15[i]>>1) + \ NDeltaMin_Q15[k] 3064 /_ 3065 k=0 3066 d_LPC 3067 __ 3068 max_center_Q15 = 32768 - (NDeltaMin_Q15[i]>>1) - \ NDeltaMin_Q15[k] 3069 /_ 3070 k=i+1 3071 center_freq_Q15 = clamp(min_center_Q15[i], 3072 (NLSF_Q15[i-1] + NLSF_Q15[i] + 1)>>1, 3073 max_center_Q15[i]) 3074 3075 NLSF_Q15[i-1] = center_freq_Q15 - (NDeltaMin_Q15[i]>>1) 3076 3077 NLSF_Q15[i] = NLSF_Q15[i-1] + NDeltaMin_Q15[i] . 3078 ]]></artwork> 3079 </figure> 3080 Then the procedure repeats again, until it has either executed 20 times or 3081 has stopped because the coefficients satisfy all the constraints. 3082 </t> 3083 <t> 3084 After the 20th repetition of the above procedure, the following fallback 3085 procedure executes once. 3086 First, the values of NLSF_Q15[k] for 0 <= k < d_LPC 3087 are sorted in ascending order. 3088 Then for each value of k from 0 to d_LPC-1, NLSF_Q15[k] is set to 3089 <figure align="center"> 3090 <artwork align="center"><![CDATA[ 3091 max(NLSF_Q15[k], NLSF_Q15[k-1] + NDeltaMin_Q15[k]) . 3092 ]]></artwork> 3093 </figure> 3094 Next, for each value of k from d_LPC-1 down to 0, NLSF_Q15[k] is set to 3095 <figure align="center"> 3096 <artwork align="center"><![CDATA[ 3097 min(NLSF_Q15[k], NLSF_Q15[k+1] - NDeltaMin_Q15[k+1]) . 3098 ]]></artwork> 3099 </figure> 3100 </t> 3101 3102 </section> 3103 3104 <section anchor="silk_nlsf_interpolation" title="Normalized LSF Interpolation"> 3105 <t> 3106 For 20 ms SILK frames, the first half of the frame (i.e., the first two 3107 subframes) may use normalized LSF coefficients that are interpolated between 3108 the decoded LSFs for the most recent coded frame (in the same channel) and the 3109 current frame. 3110 A Q2 interpolation factor follows the LSF coefficient indices in the bitstream, 3111 which is decoded using the PDF in <xref target="silk_nlsf_interp_pdf"/>. 3112 This happens in silk_decode_indices() (decode_indices.c). 3113 After either 3114 <list style="symbols"> 3115 <t>An uncoded regular SILK frame in the side channel, or</t> 3116 <t>A decoder reset (see <xref target="decoder-reset"/>),</t> 3117 </list> 3118 the decoder still decodes this factor, but ignores its value and always uses 3119 4 instead. 3120 For 10 ms SILK frames, this factor is not stored at all. 3121 </t> 3122 3123 <texttable anchor="silk_nlsf_interp_pdf" 3124 title="PDF for Normalized LSF Interpolation Index"> 3125 <ttcol>PDF</ttcol> 3126 <c>{13, 22, 29, 11, 181}/256</c> 3127 </texttable> 3128 3129 <t> 3130 Let n2_Q15[k] be the normalized LSF coefficients decoded by the procedure in 3131 <xref target="silk_nlsfs"/>, n0_Q15[k] be the LSF coefficients 3132 decoded for the prior frame, and w_Q2 be the interpolation factor. 3133 Then the normalized LSF coefficients used for the first half of a 20 ms 3134 frame, n1_Q15[k], are 3135 <figure align="center"> 3136 <artwork align="center"><![CDATA[ 3137 n1_Q15[k] = n0_Q15[k] + (w_Q2*(n2_Q15[k] - n0_Q15[k]) >> 2) . 3138 ]]></artwork> 3139 </figure> 3140 This interpolation is performed in silk_decode_parameters() 3141 (decode_parameters.c). 3142 </t> 3143 </section> 3144 3145 <section anchor="silk_nlsf2lpc" 3146 title="Converting Normalized LSFs to LPC Coefficients"> 3147 <t> 3148 Any LPC filter A(z) can be split into a symmetric part P(z) and an 3149 anti-symmetric part Q(z) such that 3150 <figure align="center"> 3151 <artwork align="center"><![CDATA[ 3152 d_LPC 3153 __ -k 1 3154 A(z) = 1 - \ a[k] * z = - * (P(z) + Q(z)) 3155 /_ 2 3156 k=1 3157 ]]></artwork> 3158 </figure> 3159 with 3160 <figure align="center"> 3161 <artwork align="center"><![CDATA[ 3162 -d_LPC-1 -1 3163 P(z) = A(z) + z * A(z ) 3164 3165 -d_LPC-1 -1 3166 Q(z) = A(z) - z * A(z ) . 3167 ]]></artwork> 3168 </figure> 3169 The even normalized LSF coefficients correspond to a pair of conjugate roots of 3170 P(z), while the odd coefficients correspond to a pair of conjugate roots of 3171 Q(z), all of which lie on the unit circle. 3172 In addition, P(z) has a root at pi and Q(z) has a root at 0. 3173 Thus, they may be reconstructed mathematically from a set of normalized LSF 3174 coefficients, n[k], as 3175 <figure align="center"> 3176 <artwork align="center"><![CDATA[ 3177 d_LPC/2-1 3178 -1 ___ -1 -2 3179 P(z) = (1 + z ) * | | (1 - 2*cos(pi*n[2*k])*z + z ) 3180 k=0 3181 3182 d_LPC/2-1 3183 -1 ___ -1 -2 3184 Q(z) = (1 - z ) * | | (1 - 2*cos(pi*n[2*k+1])*z + z ) 3185 k=0 3186 ]]></artwork> 3187 </figure> 3188 </t> 3189 <t> 3190 However, SILK performs this reconstruction using a fixed-point approximation so 3191 that all decoders can reproduce it in a bit-exact manner to avoid prediction 3192 drift. 3193 The function silk_NLSF2A() (NLSF2A.c) implements this procedure. 3194 </t> 3195 <t> 3196 To start, it approximates cos(pi*n[k]) using a table lookup with linear 3197 interpolation. 3198 The encoder SHOULD use the inverse of this piecewise linear approximation, 3199 rather than the true inverse of the cosine function, when deriving the 3200 normalized LSF coefficients. 3201 These values are also re-ordered to improve numerical accuracy when 3202 constructing the LPC polynomials. 3203 </t> 3204 3205 <texttable anchor="silk_nlsf_orderings" 3206 title="LSF Ordering for Polynomial Evaluation"> 3207 <ttcol>Coefficient</ttcol> 3208 <ttcol align="right">NB and MB</ttcol> 3209 <ttcol align="right">WB</ttcol> 3210 <c>0</c> <c>0</c> <c>0</c> 3211 <c>1</c> <c>9</c> <c>15</c> 3212 <c>2</c> <c>6</c> <c>8</c> 3213 <c>3</c> <c>3</c> <c>7</c> 3214 <c>4</c> <c>4</c> <c>4</c> 3215 <c>5</c> <c>5</c> <c>11</c> 3216 <c>6</c> <c>8</c> <c>12</c> 3217 <c>7</c> <c>1</c> <c>3</c> 3218 <c>8</c> <c>2</c> <c>2</c> 3219 <c>9</c> <c>7</c> <c>13</c> 3220 <c>10</c> <c/> <c>10</c> 3221 <c>11</c> <c/> <c>5</c> 3222 <c>12</c> <c/> <c>6</c> 3223 <c>13</c> <c/> <c>9</c> 3224 <c>14</c> <c/> <c>14</c> 3225 <c>15</c> <c/> <c>1</c> 3226 </texttable> 3227 3228 <t> 3229 The top 7 bits of each normalized LSF coefficient index a value in the table, 3230 and the next 8 bits interpolate between it and the next value. 3231 Let i = (n[k] >> 8) be the integer index and 3232 f = (n[k] & 255) be the fractional part of a given 3233 coefficient. 3234 Then the re-ordered, approximated cosine, c_Q17[ordering[k]], is 3235 <figure align="center"> 3236 <artwork align="center"><![CDATA[ 3237 c_Q17[ordering[k]] = (cos_Q12[i]*256 3238 + (cos_Q12[i+1]-cos_Q12[i])*f + 4) >> 3 , 3239 ]]></artwork> 3240 </figure> 3241 where ordering[k] is the k'th entry of the column of 3242 <xref target="silk_nlsf_orderings"/> corresponding to the current audio 3243 bandwidth and cos_Q12[i] is the i'th entry of <xref target="silk_cos_table"/>. 3244 </t> 3245 3246 <texttable anchor="silk_cos_table" 3247 title="Q12 Cosine Table for LSF Conversion"> 3248 <ttcol align="right">i</ttcol> 3249 <ttcol align="right">+0</ttcol> 3250 <ttcol align="right">+1</ttcol> 3251 <ttcol align="right">+2</ttcol> 3252 <ttcol align="right">+3</ttcol> 3253 <c>0</c> 3254 <c>4096</c> <c>4095</c> <c>4091</c> <c>4085</c> 3255 <c>4</c> 3256 <c>4076</c> <c>4065</c> <c>4052</c> <c>4036</c> 3257 <c>8</c> 3258 <c>4017</c> <c>3997</c> <c>3973</c> <c>3948</c> 3259 <c>12</c> 3260 <c>3920</c> <c>3889</c> <c>3857</c> <c>3822</c> 3261 <c>16</c> 3262 <c>3784</c> <c>3745</c> <c>3703</c> <c>3659</c> 3263 <c>20</c> 3264 <c>3613</c> <c>3564</c> <c>3513</c> <c>3461</c> 3265 <c>24</c> 3266 <c>3406</c> <c>3349</c> <c>3290</c> <c>3229</c> 3267 <c>28</c> 3268 <c>3166</c> <c>3102</c> <c>3035</c> <c>2967</c> 3269 <c>32</c> 3270 <c>2896</c> <c>2824</c> <c>2751</c> <c>2676</c> 3271 <c>36</c> 3272 <c>2599</c> <c>2520</c> <c>2440</c> <c>2359</c> 3273 <c>40</c> 3274 <c>2276</c> <c>2191</c> <c>2106</c> <c>2019</c> 3275 <c>44</c> 3276 <c>1931</c> <c>1842</c> <c>1751</c> <c>1660</c> 3277 <c>48</c> 3278 <c>1568</c> <c>1474</c> <c>1380</c> <c>1285</c> 3279 <c>52</c> 3280 <c>1189</c> <c>1093</c> <c>995</c> <c>897</c> 3281 <c>56</c> 3282 <c>799</c> <c>700</c> <c>601</c> <c>501</c> 3283 <c>60</c> 3284 <c>401</c> <c>301</c> <c>201</c> <c>101</c> 3285 <c>64</c> 3286 <c>0</c> <c>-101</c> <c>-201</c> <c>-301</c> 3287 <c>68</c> 3288 <c>-401</c> <c>-501</c> <c>-601</c> <c>-700</c> 3289 <c>72</c> 3290 <c>-799</c> <c>-897</c> <c>-995</c> <c>-1093</c> 3291 <c>76</c> 3292 <c>-1189</c><c>-1285</c><c>-1380</c><c>-1474</c> 3293 <c>80</c> 3294 <c>-1568</c><c>-1660</c><c>-1751</c><c>-1842</c> 3295 <c>84</c> 3296 <c>-1931</c><c>-2019</c><c>-2106</c><c>-2191</c> 3297 <c>88</c> 3298 <c>-2276</c><c>-2359</c><c>-2440</c><c>-2520</c> 3299 <c>92</c> 3300 <c>-2599</c><c>-2676</c><c>-2751</c><c>-2824</c> 3301 <c>96</c> 3302 <c>-2896</c><c>-2967</c><c>-3035</c><c>-3102</c> 3303 <c>100</c> 3304 <c>-3166</c><c>-3229</c><c>-3290</c><c>-3349</c> 3305 <c>104</c> 3306 <c>-3406</c><c>-3461</c><c>-3513</c><c>-3564</c> 3307 <c>108</c> 3308 <c>-3613</c><c>-3659</c><c>-3703</c><c>-3745</c> 3309 <c>112</c> 3310 <c>-3784</c><c>-3822</c><c>-3857</c><c>-3889</c> 3311 <c>116</c> 3312 <c>-3920</c><c>-3948</c><c>-3973</c><c>-3997</c> 3313 <c>120</c> 3314 <c>-4017</c><c>-4036</c><c>-4052</c><c>-4065</c> 3315 <c>124</c> 3316 <c>-4076</c><c>-4085</c><c>-4091</c><c>-4095</c> 3317 <c>128</c> 3318 <c>-4096</c> <c/> <c/> <c/> 3319 </texttable> 3320 3321 <t> 3322 Given the list of cosine values, silk_NLSF2A_find_poly() (NLSF2A.c) 3323 computes the coefficients of P and Q, described here via a simple recurrence. 3324 Let p_Q16[k][j] and q_Q16[k][j] be the coefficients of the products of the 3325 first (k+1) root pairs for P and Q, with j indexing the coefficient number. 3326 Only the first (k+2) coefficients are needed, as the products are symmetric. 3327 Let p_Q16[0][0] = q_Q16[0][0] = 1<<16, 3328 p_Q16[0][1] = -c_Q17[0], q_Q16[0][1] = -c_Q17[1], and 3329 d2 = d_LPC/2. 3330 As boundary conditions, assume 3331 p_Q16[k][j] = q_Q16[k][j] = 0 for all 3332 j < 0. 3333 Also, assume p_Q16[k][k+2] = p_Q16[k][k] and 3334 q_Q16[k][k+2] = q_Q16[k][k] (because of the symmetry). 3335 Then, for 0 < k < d2 and 0 <= j <= k+1, 3336 <figure align="center"> 3337 <artwork align="center"><![CDATA[ 3338 p_Q16[k][j] = p_Q16[k-1][j] + p_Q16[k-1][j-2] 3339 - ((c_Q17[2*k]*p_Q16[k-1][j-1] + 32768)>>16) , 3340 3341 q_Q16[k][j] = q_Q16[k-1][j] + q_Q16[k-1][j-2] 3342 - ((c_Q17[2*k+1]*q_Q16[k-1][j-1] + 32768)>>16) . 3343 ]]></artwork> 3344 </figure> 3345 The use of Q17 values for the cosine terms in an otherwise Q16 expression 3346 implicitly scales them by a factor of 2. 3347 The multiplications in this recurrence may require up to 48 bits of precision 3348 in the result to avoid overflow. 3349 In practice, each row of the recurrence only depends on the previous row, so an 3350 implementation does not need to store all of them. 3351 </t> 3352 <t> 3353 silk_NLSF2A() uses the values from the last row of this recurrence to 3354 reconstruct a 32-bit version of the LPC filter (without the leading 1.0 3355 coefficient), a32_Q17[k], 0 <= k < d2: 3356 <figure align="center"> 3357 <artwork align="center"><![CDATA[ 3358 a32_Q17[k] = -(q_Q16[d2-1][k+1] - q_Q16[d2-1][k]) 3359 - (p_Q16[d2-1][k+1] + p_Q16[d2-1][k])) , 3360 3361 a32_Q17[d_LPC-k-1] = (q_Q16[d2-1][k+1] - q_Q16[d2-1][k]) 3362 - (p_Q16[d2-1][k+1] + p_Q16[d2-1][k])) . 3363 ]]></artwork> 3364 </figure> 3365 The sum and difference of two terms from each of the p_Q16 and q_Q16 3366 coefficient lists reflect the (1 + z**-1) and 3367 (1 - z**-1) factors of P and Q, respectively. 3368 The promotion of the expression from Q16 to Q17 implicitly scales the result 3369 by 1/2. 3370 </t> 3371 </section> 3372 3373 <section anchor="silk_lpc_range_limit" 3374 title="Limiting the Range of the LPC Coefficients"> 3375 <t> 3376 The a32_Q17[] coefficients are too large to fit in a 16-bit value, which 3377 significantly increases the cost of applying this filter in fixed-point 3378 decoders. 3379 Reducing them to Q12 precision doesn't incur any significant quality loss, 3380 but still does not guarantee they will fit. 3381 silk_NLSF2A() applies up to 10 rounds of bandwidth expansion to limit 3382 the dynamic range of these coefficients. 3383 Even floating-point decoders SHOULD perform these steps, to avoid mismatch. 3384 </t> 3385 <t> 3386 For each round, the process first finds the index k such that abs(a32_Q17[k]) 3387 is largest, breaking ties by choosing the lowest value of k. 3388 Then, it computes the corresponding Q12 precision value, maxabs_Q12, subject to 3389 an upper bound to avoid overflow in subsequent computations: 3390 <figure align="center"> 3391 <artwork align="center"><![CDATA[ 3392 maxabs_Q12 = min((maxabs_Q17 + 16) >> 5, 163838) . 3393 ]]></artwork> 3394 </figure> 3395 If this is larger than 32767, the procedure derives the chirp factor, 3396 sc_Q16[0], to use in the bandwidth expansion as 3397 <figure align="center"> 3398 <artwork align="center"><![CDATA[ 3399 (maxabs_Q12 - 32767) << 14 3400 sc_Q16[0] = 65470 - -------------------------- , 3401 (maxabs_Q12 * (k+1)) >> 2 3402 ]]></artwork> 3403 </figure> 3404 where the division here is integer division. 3405 This is an approximation of the chirp factor needed to reduce the target 3406 coefficient to 32767, though it is both less than 0.999 and, for 3407 k > 0 when maxabs_Q12 is much greater than 32767, still slightly 3408 too large. 3409 The upper bound on maxabs_Q12, 163838, was chosen because it is equal to 3410 ((2**31 - 1) >> 14) + 32767, i.e., the 3411 largest value of maxabs_Q12 that would not overflow the numerator in the 3412 equation above when stored in a signed 32-bit integer. 3413 </t> 3414 <t> 3415 silk_bwexpander_32() (bwexpander_32.c) performs the bandwidth expansion (again, 3416 only when maxabs_Q12 is greater than 32767) using the following recurrence: 3417 <figure align="center"> 3418 <artwork align="center"><![CDATA[ 3419 a32_Q17[k] = (a32_Q17[k]*sc_Q16[k]) >> 16 3420 3421 sc_Q16[k+1] = (sc_Q16[0]*sc_Q16[k] + 32768) >> 16 3422 ]]></artwork> 3423 </figure> 3424 The first multiply may require up to 48 bits of precision in the result to 3425 avoid overflow. 3426 The second multiply must be unsigned to avoid overflow with only 32 bits of 3427 precision. 3428 The reference implementation uses a slightly more complex formulation that 3429 avoids the 32-bit overflow using signed multiplication, but is otherwise 3430 equivalent. 3431 </t> 3432 <t> 3433 After 10 rounds of bandwidth expansion are performed, they are simply saturated 3434 to 16 bits: 3435 <figure align="center"> 3436 <artwork align="center"><![CDATA[ 3437 a32_Q17[k] = clamp(-32768, (a32_Q17[k] + 16) >> 5, 32767) << 5 . 3438 ]]></artwork> 3439 </figure> 3440 Because this performs the actual saturation in the Q12 domain, but converts the 3441 coefficients back to the Q17 domain for the purposes of prediction gain 3442 limiting, this step must be performed after the 10th round of bandwidth 3443 expansion, regardless of whether or not the Q12 version of any coefficient 3444 still overflows a 16-bit integer. 3445 This saturation is not performed if maxabs_Q12 drops to 32767 or less prior to 3446 the 10th round. 3447 </t> 3448 </section> 3449 3450 <section anchor="silk_lpc_gain_limit" 3451 title="Limiting the Prediction Gain of the LPC Filter"> 3452 <t> 3453 The prediction gain of an LPC synthesis filter is the square-root of the output 3454 energy when the filter is excited by a unit-energy impulse. 3455 Even if the Q12 coefficients would fit, the resulting filter may still have a 3456 significant gain (especially for voiced sounds), making the filter unstable. 3457 silk_NLSF2A() applies up to 18 additional rounds of bandwidth expansion to 3458 limit the prediction gain. 3459 Instead of controlling the amount of bandwidth expansion using the prediction 3460 gain itself (which may diverge to infinity for an unstable filter), 3461 silk_NLSF2A() uses silk_LPC_inverse_pred_gain_QA() (LPC_inv_pred_gain.c) to 3462 compute the reflection coefficients associated with the filter. 3463 The filter is stable if and only if the magnitude of these coefficients is 3464 sufficiently less than one. 3465 The reflection coefficients, rc[k], can be computed using a simple Levinson 3466 recurrence, initialized with the LPC coefficients 3467 a[d_LPC-1][n] = a[n], and then updated via 3468 <figure align="center"> 3469 <artwork align="center"><![CDATA[ 3470 rc[k] = -a[k][k] , 3471 3472 a[k][n] - a[k][k-n-1]*rc[k] 3473 a[k-1][n] = --------------------------- . 3474 2 3475 1 - rc[k] 3476 ]]></artwork> 3477 </figure> 3478 </t> 3479 <t> 3480 However, silk_LPC_inverse_pred_gain_QA() approximates this using fixed-point 3481 arithmetic to guarantee reproducible results across platforms and 3482 implementations. 3483 Since small changes in the coefficients can make a stable filter unstable, it 3484 takes the real Q12 coefficients that will be used during reconstruction as 3485 input. 3486 Thus, let 3487 <figure align="center"> 3488 <artwork align="center"><![CDATA[ 3489 a32_Q12[n] = (a32_Q17[n] + 16) >> 5 3490 ]]></artwork> 3491 </figure> 3492 be the Q12 version of the LPC coefficients that will eventually be used. 3493 As a simple initial check, the decoder computes the DC response as 3494 <figure align="center"> 3495 <artwork align="center"><![CDATA[ 3496 d_PLC-1 3497 __ 3498 DC_resp = \ a32_Q12[n] 3499 /_ 3500 n=0 3501 ]]></artwork> 3502 </figure> 3503 and if DC_resp > 4096, the filter is unstable. 3504 </t> 3505 <t> 3506 Increasing the precision of these Q12 coefficients to Q24 for intermediate 3507 computations allows more accurate computation of the reflection coefficients, 3508 so the decoder initializes the recurrence via 3509 <figure align="center"> 3510 <artwork align="center"><![CDATA[ 3511 a32_Q24[d_LPC-1][n] = a32_Q12[n] << 12 . 3512 ]]></artwork> 3513 </figure> 3514 Then for each k from d_LPC-1 down to 0, if 3515 abs(a32_Q24[k][k]) > 16773022, the filter is unstable and the 3516 recurrence stops. 3517 The constant 16773022 here is approximately 0.99975 in Q24. 3518 Otherwise, row k-1 of a32_Q24 is computed from row k as 3519 <figure align="center"> 3520 <artwork align="center"><![CDATA[ 3521 rc_Q31[k] = -a32_Q24[k][k] << 7 , 3522 3523 div_Q30[k] = (1<<30) - (rc_Q31[k]*rc_Q31[k] >> 32) , 3524 3525 b1[k] = ilog(div_Q30[k]) , 3526 3527 b2[k] = b1[k] - 16 , 3528 3529 (1<<29) - 1 3530 inv_Qb2[k] = ----------------------- , 3531 div_Q30[k] >> (b2[k]+1) 3532 3533 err_Q29[k] = (1<<29) 3534 - ((div_Q30[k]<<(15-b2[k]))*inv_Qb2[k] >> 16) , 3535 3536 gain_Qb1[k] = ((inv_Qb2[k] << 16) 3537 + (err_Q29[k]*inv_Qb2[k] >> 13)) , 3538 3539 num_Q24[k-1][n] = a32_Q24[k][n] 3540 - ((a32_Q24[k][k-n-1]*rc_Q31[k] + (1<<30)) >> 31) , 3541 3542 a32_Q24[k-1][n] = (num_Q24[k-1][n]*gain_Qb1[k] 3543 + (1<<(b1[k]-1))) >> b1[k] , 3544 ]]></artwork> 3545 </figure> 3546 where 0 <= n < k. 3547 Here, rc_Q30[k] are the reflection coefficients. 3548 div_Q30[k] is the denominator for each iteration, and gain_Qb1[k] is its 3549 multiplicative inverse (with b1[k] fractional bits, where b1[k] ranges from 3550 20 to 31). 3551 inv_Qb2[k], which ranges from 16384 to 32767, is a low-precision version of 3552 that inverse (with b2[k] fractional bits). 3553 err_Q29[k] is the residual error, ranging from -32763 to 32392, which is used 3554 to improve the accuracy. 3555 The values t_Q24[k-1][n] for each n are the numerators for the next row of 3556 coefficients in the recursion, and a32_Q24[k-1][n] is the final version of 3557 that row. 3558 Every multiply in this procedure except the one used to compute gain_Qb1[k] 3559 requires more than 32 bits of precision, but otherwise all intermediate 3560 results fit in 32 bits or less. 3561 In practice, because each row only depends on the next one, an implementation 3562 does not need to store them all. 3563 </t> 3564 <t> 3565 If abs(a32_Q24[k][k]) <= 16773022 for 3566 0 <= k < d_LPC, then the filter is considered stable. 3567 However, the problem of determining stability is ill-conditioned when the 3568 filter contains several reflection coefficients whose magnitude is very close 3569 to one. 3570 This fixed-point algorithm is not mathematically guaranteed to correctly 3571 classify filters as stable or unstable in this case, though it does very well 3572 in practice. 3573 </t> 3574 <t> 3575 On round i, 1 <= i <= 18, if the filter passes these 3576 stability checks, then this procedure stops, and the final LPC coefficients to 3577 use for reconstruction in <xref target="silk_lpc_synthesis"/> are 3578 <figure align="center"> 3579 <artwork align="center"><![CDATA[ 3580 a_Q12[k] = (a32_Q17[k] + 16) >> 5 . 3581 ]]></artwork> 3582 </figure> 3583 Otherwise, a round of bandwidth expansion is applied using the same procedure 3584 as in <xref target="silk_lpc_range_limit"/>, with 3585 <figure align="center"> 3586 <artwork align="center"><![CDATA[ 3587 sc_Q16[0] = 65536 - (2<<i) . 3588 ]]></artwork> 3589 </figure> 3590 During the 15th round, sc_Q16[0] becomes 0 in the above equation, so a_Q12[k] 3591 is set to 0 for all k, guaranteeing a stable filter. 3592 </t> 3593 </section> 3594 3595 </section> 3596 3597 <section anchor="silk_ltp_params" toc="include" 3598 title="Long-Term Prediction (LTP) Parameters"> 3599 <t> 3600 After the normalized LSF indices and, for 20 ms frames, the LSF 3601 interpolation index, voiced frames (see <xref target="silk_frame_type"/>) 3602 include additional LTP parameters. 3603 There is one primary lag index for each SILK frame, but this is refined to 3604 produce a separate lag index per subframe using a vector quantizer. 3605 Each subframe also gets its own prediction gain coefficient. 3606 </t> 3607 3608 <section anchor="silk_ltp_lags" title="Pitch Lags"> 3609 <t> 3610 The primary lag index is coded either relative to the primary lag of the prior 3611 frame in the same channel, or as an absolute index. 3612 Absolute coding is used if and only if 3613 <list style="symbols"> 3614 <t> 3615 This is the first SILK frame of its type (LBRR or regular) for this channel in 3616 the current Opus frame, 3617 </t> 3618 <t> 3619 The previous SILK frame of the same type (LBRR or regular) for this channel in 3620 the same Opus frame was not coded, or 3621 </t> 3622 <t> 3623 That previous SILK frame was coded, but was not voiced (see 3624 <xref target="silk_frame_type"/>). 3625 </t> 3626 </list> 3627 </t> 3628 3629 <t> 3630 With absolute coding, the primary pitch lag may range from 2 ms 3631 (inclusive) up to 18 ms (exclusive), corresponding to pitches from 3632 500 Hz down to 55.6 Hz, respectively. 3633 It is comprised of a high part and a low part, where the decoder reads the high 3634 part using the 32-entry codebook in <xref target="silk_abs_pitch_high_pdf"/> 3635 and the low part using the codebook corresponding to the current audio 3636 bandwidth from <xref target="silk_abs_pitch_low_pdf"/>. 3637 The final primary pitch lag is then 3638 <figure align="center"> 3639 <artwork align="center"><![CDATA[ 3640 lag = lag_high*lag_scale + lag_low + lag_min 3641 ]]></artwork> 3642 </figure> 3643 where lag_high is the high part, lag_low is the low part, and lag_scale 3644 and lag_min are the values from the "Scale" and "Minimum Lag" columns of 3645 <xref target="silk_abs_pitch_low_pdf"/>, respectively. 3646 </t> 3647 3648 <texttable anchor="silk_abs_pitch_high_pdf" 3649 title="PDF for High Part of Primary Pitch Lag"> 3650 <ttcol align="left">PDF</ttcol> 3651 <c>{3, 3, 6, 11, 21, 30, 32, 19, 3652 11, 10, 12, 13, 13, 12, 11, 9, 3653 8, 7, 6, 4, 2, 2, 2, 1, 3654 1, 1, 1, 1, 1, 1, 1, 1}/256</c> 3655 </texttable> 3656 3657 <texttable anchor="silk_abs_pitch_low_pdf" 3658 title="PDF for Low Part of Primary Pitch Lag"> 3659 <ttcol>Audio Bandwidth</ttcol> 3660 <ttcol>PDF</ttcol> 3661 <ttcol>Scale</ttcol> 3662 <ttcol>Minimum Lag</ttcol> 3663 <ttcol>Maximum Lag</ttcol> 3664 <c>NB</c> <c>{64, 64, 64, 64}/256</c> <c>4</c> <c>16</c> <c>144</c> 3665 <c>MB</c> <c>{43, 42, 43, 43, 42, 43}/256</c> <c>6</c> <c>24</c> <c>216</c> 3666 <c>WB</c> <c>{32, 32, 32, 32, 32, 32, 32, 32}/256</c> <c>8</c> <c>32</c> <c>288</c> 3667 </texttable> 3668 3669 <t> 3670 All frames that do not use absolute coding for the primary lag index use 3671 relative coding instead. 3672 The decoder reads a single delta value using the 21-entry PDF in 3673 <xref target="silk_rel_pitch_pdf"/>. 3674 If the resulting value is zero, it falls back to the absolute coding procedure 3675 from the prior paragraph. 3676 Otherwise, the final primary pitch lag is then 3677 <figure align="center"> 3678 <artwork align="center"><![CDATA[ 3679 lag = previous_lag + (delta_lag_index - 9) 3680 ]]></artwork> 3681 </figure> 3682 where previous_lag is the primary pitch lag from the most recent frame in the 3683 same channel and delta_lag_index is the value just decoded. 3684 This allows a per-frame change in the pitch lag of -8 to +11 samples. 3685 The decoder does no clamping at this point, so this value can fall outside the 3686 range of 2 ms to 18 ms, and the decoder must use this unclamped 3687 value when using relative coding in the next SILK frame (if any). 3688 However, because an Opus frame can use relative coding for at most two 3689 consecutive SILK frames, integer overflow should not be an issue. 3690 </t> 3691 3692 <texttable anchor="silk_rel_pitch_pdf" 3693 title="PDF for Primary Pitch Lag Change"> 3694 <ttcol align="left">PDF</ttcol> 3695 <c>{46, 2, 2, 3, 4, 6, 10, 15, 3696 26, 38, 30, 22, 15, 10, 7, 6, 3697 4, 4, 2, 2, 2}/256</c> 3698 </texttable> 3699 3700 <t> 3701 After the primary pitch lag, a "pitch contour", stored as a single entry from 3702 one of four small VQ codebooks, gives lag offsets for each subframe in the 3703 current SILK frame. 3704 The codebook index is decoded using one of the PDFs in 3705 <xref target="silk_pitch_contour_pdfs"/> depending on the current frame size 3706 and audio bandwidth. 3707 Tables <xref format="counter" target="silk_pitch_contour_cb_nb10ms"/> 3708 through <xref format="counter" target="silk_pitch_contour_cb_mbwb20ms"/> 3709 give the corresponding offsets to apply to the primary pitch lag for each 3710 subframe given the decoded codebook index. 3711 </t> 3712 3713 <texttable anchor="silk_pitch_contour_pdfs" 3714 title="PDFs for Subframe Pitch Contour"> 3715 <ttcol>Audio Bandwidth</ttcol> 3716 <ttcol>SILK Frame Size</ttcol> 3717 <ttcol align="right">Codebook Size</ttcol> 3718 <ttcol>PDF</ttcol> 3719 <c>NB</c> <c>10 ms</c> <c>3</c> 3720 <c>{143, 50, 63}/256</c> 3721 <c>NB</c> <c>20 ms</c> <c>11</c> 3722 <c>{68, 12, 21, 17, 19, 22, 30, 24, 3723 17, 16, 10}/256</c> 3724 <c>MB or WB</c> <c>10 ms</c> <c>12</c> 3725 <c>{91, 46, 39, 19, 14, 12, 8, 7, 3726 6, 5, 5, 4}/256</c> 3727 <c>MB or WB</c> <c>20 ms</c> <c>34</c> 3728 <c>{33, 22, 18, 16, 15, 14, 14, 13, 3729 13, 10, 9, 9, 8, 6, 6, 6, 3730 5, 4, 4, 4, 3, 3, 3, 2, 3731 2, 2, 2, 2, 2, 2, 1, 1, 3732 1, 1}/256</c> 3733 </texttable> 3734 3735 <texttable anchor="silk_pitch_contour_cb_nb10ms" 3736 title="Codebook Vectors for Subframe Pitch Contour: NB, 10 ms Frames"> 3737 <ttcol>Index</ttcol> 3738 <ttcol align="right">Subframe Offsets</ttcol> 3739 <c>0</c> <c><spanx style="vbare"> 0 0</spanx></c> 3740 <c>1</c> <c><spanx style="vbare"> 1 0</spanx></c> 3741 <c>2</c> <c><spanx style="vbare"> 0 1</spanx></c> 3742 </texttable> 3743 3744 <texttable anchor="silk_pitch_contour_cb_nb20ms" 3745 title="Codebook Vectors for Subframe Pitch Contour: NB, 20 ms Frames"> 3746 <ttcol>Index</ttcol> 3747 <ttcol align="right">Subframe Offsets</ttcol> 3748 <c>0</c> <c><spanx style="vbare"> 0 0 0 0</spanx></c> 3749 <c>1</c> <c><spanx style="vbare"> 2 1 0 -1</spanx></c> 3750 <c>2</c> <c><spanx style="vbare">-1 0 1 2</spanx></c> 3751 <c>3</c> <c><spanx style="vbare">-1 0 0 1</spanx></c> 3752 <c>4</c> <c><spanx style="vbare">-1 0 0 0</spanx></c> 3753 <c>5</c> <c><spanx style="vbare"> 0 0 0 1</spanx></c> 3754 <c>6</c> <c><spanx style="vbare"> 0 0 1 1</spanx></c> 3755 <c>7</c> <c><spanx style="vbare"> 1 1 0 0</spanx></c> 3756 <c>8</c> <c><spanx style="vbare"> 1 0 0 0</spanx></c> 3757 <c>9</c> <c><spanx style="vbare"> 0 0 0 -1</spanx></c> 3758 <c>10</c> <c><spanx style="vbare"> 1 0 0 -1</spanx></c> 3759 </texttable> 3760 3761 <texttable anchor="silk_pitch_contour_cb_mbwb10ms" 3762 title="Codebook Vectors for Subframe Pitch Contour: MB or WB, 10 ms Frames"> 3763 <ttcol>Index</ttcol> 3764 <ttcol align="right">Subframe Offsets</ttcol> 3765 <c>0</c> <c><spanx style="vbare"> 0 0</spanx></c> 3766 <c>1</c> <c><spanx style="vbare"> 0 1</spanx></c> 3767 <c>2</c> <c><spanx style="vbare"> 1 0</spanx></c> 3768 <c>3</c> <c><spanx style="vbare">-1 1</spanx></c> 3769 <c>4</c> <c><spanx style="vbare"> 1 -1</spanx></c> 3770 <c>5</c> <c><spanx style="vbare">-1 2</spanx></c> 3771 <c>6</c> <c><spanx style="vbare"> 2 -1</spanx></c> 3772 <c>7</c> <c><spanx style="vbare">-2 2</spanx></c> 3773 <c>8</c> <c><spanx style="vbare"> 2 -2</spanx></c> 3774 <c>9</c> <c><spanx style="vbare">-2 3</spanx></c> 3775 <c>10</c> <c><spanx style="vbare"> 3 -2</spanx></c> 3776 <c>11</c> <c><spanx style="vbare">-3 3</spanx></c> 3777 </texttable> 3778 3779 <texttable anchor="silk_pitch_contour_cb_mbwb20ms" 3780 title="Codebook Vectors for Subframe Pitch Contour: MB or WB, 20 ms Frames"> 3781 <ttcol>Index</ttcol> 3782 <ttcol align="right">Subframe Offsets</ttcol> 3783 <c>0</c> <c><spanx style="vbare"> 0 0 0 0</spanx></c> 3784 <c>1</c> <c><spanx style="vbare"> 0 0 1 1</spanx></c> 3785 <c>2</c> <c><spanx style="vbare"> 1 1 0 0</spanx></c> 3786 <c>3</c> <c><spanx style="vbare">-1 0 0 0</spanx></c> 3787 <c>4</c> <c><spanx style="vbare"> 0 0 0 1</spanx></c> 3788 <c>5</c> <c><spanx style="vbare"> 1 0 0 0</spanx></c> 3789 <c>6</c> <c><spanx style="vbare">-1 0 0 1</spanx></c> 3790 <c>7</c> <c><spanx style="vbare"> 0 0 0 -1</spanx></c> 3791 <c>8</c> <c><spanx style="vbare">-1 0 1 2</spanx></c> 3792 <c>9</c> <c><spanx style="vbare"> 1 0 0 -1</spanx></c> 3793 <c>10</c> <c><spanx style="vbare">-2 -1 1 2</spanx></c> 3794 <c>11</c> <c><spanx style="vbare"> 2 1 0 -1</spanx></c> 3795 <c>12</c> <c><spanx style="vbare">-2 0 0 2</spanx></c> 3796 <c>13</c> <c><spanx style="vbare">-2 0 1 3</spanx></c> 3797 <c>14</c> <c><spanx style="vbare"> 2 1 -1 -2</spanx></c> 3798 <c>15</c> <c><spanx style="vbare">-3 -1 1 3</spanx></c> 3799 <c>16</c> <c><spanx style="vbare"> 2 0 0 -2</spanx></c> 3800 <c>17</c> <c><spanx style="vbare"> 3 1 0 -2</spanx></c> 3801 <c>18</c> <c><spanx style="vbare">-3 -1 2 4</spanx></c> 3802 <c>19</c> <c><spanx style="vbare">-4 -1 1 4</spanx></c> 3803 <c>20</c> <c><spanx style="vbare"> 3 1 -1 -3</spanx></c> 3804 <c>21</c> <c><spanx style="vbare">-4 -1 2 5</spanx></c> 3805 <c>22</c> <c><spanx style="vbare"> 4 2 -1 -3</spanx></c> 3806 <c>23</c> <c><spanx style="vbare"> 4 1 -1 -4</spanx></c> 3807 <c>24</c> <c><spanx style="vbare">-5 -1 2 6</spanx></c> 3808 <c>25</c> <c><spanx style="vbare"> 5 2 -1 -4</spanx></c> 3809 <c>26</c> <c><spanx style="vbare">-6 -2 2 6</spanx></c> 3810 <c>27</c> <c><spanx style="vbare">-5 -2 2 5</spanx></c> 3811 <c>28</c> <c><spanx style="vbare"> 6 2 -1 -5</spanx></c> 3812 <c>29</c> <c><spanx style="vbare">-7 -2 3 8</spanx></c> 3813 <c>30</c> <c><spanx style="vbare"> 6 2 -2 -6</spanx></c> 3814 <c>31</c> <c><spanx style="vbare"> 5 2 -2 -5</spanx></c> 3815 <c>32</c> <c><spanx style="vbare"> 8 3 -2 -7</spanx></c> 3816 <c>33</c> <c><spanx style="vbare">-9 -3 3 9</spanx></c> 3817 </texttable> 3818 3819 <t> 3820 The final pitch lag for each subframe is assembled in silk_decode_pitch() 3821 (decode_pitch.c). 3822 Let lag be the primary pitch lag for the current SILK frame, contour_index be 3823 index of the VQ codebook, and lag_cb[contour_index][k] be the corresponding 3824 entry of the codebook from the appropriate table given above for the k'th 3825 subframe. 3826 Then the final pitch lag for that subframe is 3827 <figure align="center"> 3828 <artwork align="center"><![CDATA[ 3829 pitch_lags[k] = clamp(lag_min, lag + lag_cb[contour_index][k], 3830 lag_max) 3831 ]]></artwork> 3832 </figure> 3833 where lag_min and lag_max are the values from the "Minimum Lag" and 3834 "Maximum Lag" columns of <xref target="silk_abs_pitch_low_pdf"/>, 3835 respectively. 3836 </t> 3837 3838 </section> 3839 3840 <section anchor="silk_ltp_filter" title="LTP Filter Coefficients"> 3841 <t> 3842 SILK uses a separate 5-tap pitch filter for each subframe, selected from one 3843 of three codebooks. 3844 The three codebooks each represent different rate-distortion trade-offs, with 3845 average rates of 1.61 bits/subframe, 3.68 bits/subframe, and 3846 4.85 bits/subframe, respectively. 3847 </t> 3848 3849 <t> 3850 The importance of the filter coefficients generally depends on two factors: the 3851 periodicity of the signal and relative energy between the current subframe and 3852 the signal from one period earlier. 3853 Greater periodicity and decaying energy both lead to more important filter 3854 coefficients, and thus should be coded with lower distortion and higher rate. 3855 These properties are relatively stable over the duration of a single SILK 3856 frame, hence all of the subframes in a SILK frame choose their filter from the 3857 same codebook. 3858 This is signaled with an explicitly-coded "periodicity index". 3859 This immediately follows the subframe pitch lags, and is coded using the 3860 3-entry PDF from <xref target="silk_perindex_pdf"/>. 3861 </t> 3862 3863 <texttable anchor="silk_perindex_pdf" title="Periodicity Index PDF"> 3864 <ttcol>PDF</ttcol> 3865 <c>{77, 80, 99}/256</c> 3866 </texttable> 3867 3868 <t> 3869 The indices of the filters for each subframe follow. 3870 They are all coded using the PDF from <xref target="silk_ltp_filter_pdfs"/> 3871 corresponding to the periodicity index. 3872 Tables <xref format="counter" target="silk_ltp_filter_coeffs0"/> 3873 through <xref format="counter" target="silk_ltp_filter_coeffs2"/> 3874 contain the corresponding filter taps as signed Q7 integers. 3875 </t> 3876 3877 <texttable anchor="silk_ltp_filter_pdfs" title="LTP Filter PDFs"> 3878 <ttcol>Periodicity Index</ttcol> 3879 <ttcol align="right">Codebook Size</ttcol> 3880 <ttcol>PDF</ttcol> 3881 <c>0</c> <c>8</c> <c>{185, 15, 13, 13, 9, 9, 6, 6}/256</c> 3882 <c>1</c> <c>16</c> <c>{57, 34, 21, 20, 15, 13, 12, 13, 3883 10, 10, 9, 10, 9, 8, 7, 8}/256</c> 3884 <c>2</c> <c>32</c> <c>{15, 16, 14, 12, 12, 12, 11, 11, 3885 11, 10, 9, 9, 9, 9, 8, 8, 3886 8, 8, 7, 7, 6, 6, 5, 4, 3887 5, 4, 4, 4, 3, 4, 3, 2}/256</c> 3888 </texttable> 3889 3890 <texttable anchor="silk_ltp_filter_coeffs0" 3891 title="Codebook Vectors for LTP Filter, Periodicity Index 0"> 3892 <ttcol>Index</ttcol> 3893 <ttcol align="right">Filter Taps (Q7)</ttcol> 3894 <c>0</c> 3895 <c><spanx style="vbare"> 4 6 24 7 5</spanx></c> 3896 <c>1</c> 3897 <c><spanx style="vbare"> 0 0 2 0 0</spanx></c> 3898 <c>2</c> 3899 <c><spanx style="vbare"> 12 28 41 13 -4</spanx></c> 3900 <c>3</c> 3901 <c><spanx style="vbare"> -9 15 42 25 14</spanx></c> 3902 <c>4</c> 3903 <c><spanx style="vbare"> 1 -2 62 41 -9</spanx></c> 3904 <c>5</c> 3905 <c><spanx style="vbare">-10 37 65 -4 3</spanx></c> 3906 <c>6</c> 3907 <c><spanx style="vbare"> -6 4 66 7 -8</spanx></c> 3908 <c>7</c> 3909 <c><spanx style="vbare"> 16 14 38 -3 33</spanx></c> 3910 </texttable> 3911 3912 <texttable anchor="silk_ltp_filter_coeffs1" 3913 title="Codebook Vectors for LTP Filter, Periodicity Index 1"> 3914 <ttcol>Index</ttcol> 3915 <ttcol align="right">Filter Taps (Q7)</ttcol> 3916 3917 <c>0</c> 3918 <c><spanx style="vbare"> 13 22 39 23 12</spanx></c> 3919 <c>1</c> 3920 <c><spanx style="vbare"> -1 36 64 27 -6</spanx></c> 3921 <c>2</c> 3922 <c><spanx style="vbare"> -7 10 55 43 17</spanx></c> 3923 <c>3</c> 3924 <c><spanx style="vbare"> 1 1 8 1 1</spanx></c> 3925 <c>4</c> 3926 <c><spanx style="vbare"> 6 -11 74 53 -9</spanx></c> 3927 <c>5</c> 3928 <c><spanx style="vbare">-12 55 76 -12 8</spanx></c> 3929 <c>6</c> 3930 <c><spanx style="vbare"> -3 3 93 27 -4</spanx></c> 3931 <c>7</c> 3932 <c><spanx style="vbare"> 26 39 59 3 -8</spanx></c> 3933 <c>8</c> 3934 <c><spanx style="vbare"> 2 0 77 11 9</spanx></c> 3935 <c>9</c> 3936 <c><spanx style="vbare"> -8 22 44 -6 7</spanx></c> 3937 <c>10</c> 3938 <c><spanx style="vbare"> 40 9 26 3 9</spanx></c> 3939 <c>11</c> 3940 <c><spanx style="vbare"> -7 20 101 -7 4</spanx></c> 3941 <c>12</c> 3942 <c><spanx style="vbare"> 3 -8 42 26 0</spanx></c> 3943 <c>13</c> 3944 <c><spanx style="vbare">-15 33 68 2 23</spanx></c> 3945 <c>14</c> 3946 <c><spanx style="vbare"> -2 55 46 -2 15</spanx></c> 3947 <c>15</c> 3948 <c><spanx style="vbare"> 3 -1 21 16 41</spanx></c> 3949 </texttable> 3950 3951 <texttable anchor="silk_ltp_filter_coeffs2" 3952 title="Codebook Vectors for LTP Filter, Periodicity Index 2"> 3953 <ttcol>Index</ttcol> 3954 <ttcol align="right">Filter Taps (Q7)</ttcol> 3955 <c>0</c> 3956 <c><spanx style="vbare"> -6 27 61 39 5</spanx></c> 3957 <c>1</c> 3958 <c><spanx style="vbare">-11 42 88 4 1</spanx></c> 3959 <c>2</c> 3960 <c><spanx style="vbare"> -2 60 65 6 -4</spanx></c> 3961 <c>3</c> 3962 <c><spanx style="vbare"> -1 -5 73 56 1</spanx></c> 3963 <c>4</c> 3964 <c><spanx style="vbare"> -9 19 94 29 -9</spanx></c> 3965 <c>5</c> 3966 <c><spanx style="vbare"> 0 12 99 6 4</spanx></c> 3967 <c>6</c> 3968 <c><spanx style="vbare"> 8 -19 102 46 -13</spanx></c> 3969 <c>7</c> 3970 <c><spanx style="vbare"> 3 2 13 3 2</spanx></c> 3971 <c>8</c> 3972 <c><spanx style="vbare"> 9 -21 84 72 -18</spanx></c> 3973 <c>9</c> 3974 <c><spanx style="vbare">-11 46 104 -22 8</spanx></c> 3975 <c>10</c> 3976 <c><spanx style="vbare"> 18 38 48 23 0</spanx></c> 3977 <c>11</c> 3978 <c><spanx style="vbare">-16 70 83 -21 11</spanx></c> 3979 <c>12</c> 3980 <c><spanx style="vbare"> 5 -11 117 22 -8</spanx></c> 3981 <c>13</c> 3982 <c><spanx style="vbare"> -6 23 117 -12 3</spanx></c> 3983 <c>14</c> 3984 <c><spanx style="vbare"> 3 -8 95 28 4</spanx></c> 3985 <c>15</c> 3986 <c><spanx style="vbare">-10 15 77 60 -15</spanx></c> 3987 <c>16</c> 3988 <c><spanx style="vbare"> -1 4 124 2 -4</spanx></c> 3989 <c>17</c> 3990 <c><spanx style="vbare"> 3 38 84 24 -25</spanx></c> 3991 <c>18</c> 3992 <c><spanx style="vbare"> 2 13 42 13 31</spanx></c> 3993 <c>19</c> 3994 <c><spanx style="vbare"> 21 -4 56 46 -1</spanx></c> 3995 <c>20</c> 3996 <c><spanx style="vbare"> -1 35 79 -13 19</spanx></c> 3997 <c>21</c> 3998 <c><spanx style="vbare"> -7 65 88 -9 -14</spanx></c> 3999 <c>22</c> 4000 <c><spanx style="vbare"> 20 4 81 49 -29</spanx></c> 4001 <c>23</c> 4002 <c><spanx style="vbare"> 20 0 75 3 -17</spanx></c> 4003 <c>24</c> 4004 <c><spanx style="vbare"> 5 -9 44 92 -8</spanx></c> 4005 <c>25</c> 4006 <c><spanx style="vbare"> 1 -3 22 69 31</spanx></c> 4007 <c>26</c> 4008 <c><spanx style="vbare"> -6 95 41 -12 5</spanx></c> 4009 <c>27</c> 4010 <c><spanx style="vbare"> 39 67 16 -4 1</spanx></c> 4011 <c>28</c> 4012 <c><spanx style="vbare"> 0 -6 120 55 -36</spanx></c> 4013 <c>29</c> 4014 <c><spanx style="vbare">-13 44 122 4 -24</spanx></c> 4015 <c>30</c> 4016 <c><spanx style="vbare"> 81 5 11 3 7</spanx></c> 4017 <c>31</c> 4018 <c><spanx style="vbare"> 2 0 9 10 88</spanx></c> 4019 </texttable> 4020 4021 </section> 4022 4023 <section anchor="silk_ltp_scaling" title="LTP Scaling Parameter"> 4024 <t> 4025 An LTP scaling parameter appears after the LTP filter coefficients if and only 4026 if 4027 <list style="symbols"> 4028 <t>This is a voiced frame (see <xref target="silk_frame_type"/>), and</t> 4029 <t>Either 4030 <list style="symbols"> 4031 <t> 4032 This SILK frame corresponds to the first time interval of the 4033 current Opus frame for its type (LBRR or regular), or 4034 </t> 4035 <t> 4036 This is an LBRR frame where the LBRR flags (see 4037 <xref target="silk_lbrr_flags"/>) indicate the previous LBRR frame in the same 4038 channel is not coded. 4039 </t> 4040 </list> 4041 </t> 4042 </list> 4043 This allows the encoder to trade off the prediction gain between 4044 packets against the recovery time after packet loss. 4045 Unlike absolute-coding for pitch lags, regular SILK frames that are not at the 4046 start of an Opus frame (i.e., that do not correspond to the first 20 ms 4047 time interval in Opus frames of 40 or 60 ms) do not include this 4048 field, even if the prior frame was not voiced, or (in the case of the side 4049 channel) not even coded. 4050 After an uncoded frame in the side channel, the LTP buffer (see 4051 <xref target="silk_ltp_synthesis"/>) is cleared to zero, and is thus in a 4052 known state. 4053 In contrast, LBRR frames do include this field when the prior frame was not 4054 coded, since the LTP buffer contains the output of the PLC, which is 4055 non-normative. 4056 </t> 4057 <t> 4058 If present, the decoder reads a value using the 3-entry PDF in 4059 <xref target="silk_ltp_scaling_pdf"/>. 4060 The three possible values represent Q14 scale factors of 15565, 12288, and 4061 8192, respectively (corresponding to approximately 0.95, 0.75, and 0.5). 4062 Frames that do not code the scaling parameter use the default factor of 15565 4063 (approximately 0.95). 4064 </t> 4065 4066 <texttable anchor="silk_ltp_scaling_pdf" 4067 title="PDF for LTP Scaling Parameter"> 4068 <ttcol align="left">PDF</ttcol> 4069 <c>{128, 64, 64}/256</c> 4070 </texttable> 4071 4072 </section> 4073 4074 </section> 4075 4076 <section anchor="silk_seed" toc="include" 4077 title="Linear Congruential Generator (LCG) Seed"> 4078 <t> 4079 As described in <xref target="silk_excitation_reconstruction"/>, SILK uses a 4080 linear congruential generator (LCG) to inject pseudorandom noise into the 4081 quantized excitation. 4082 To ensure synchronization of this process between the encoder and decoder, each 4083 SILK frame stores a 2-bit seed after the LTP parameters (if any). 4084 The encoder may consider the choice of seed during quantization, and the 4085 flexibility of this choice lets it reduce distortion, helping to pay for the 4086 bit cost required to signal it. 4087 The decoder reads the seed using the uniform 4-entry PDF in 4088 <xref target="silk_seed_pdf"/>, yielding a value between 0 and 3, inclusive. 4089 </t> 4090 4091 <texttable anchor="silk_seed_pdf" 4092 title="PDF for LCG Seed"> 4093 <ttcol align="left">PDF</ttcol> 4094 <c>{64, 64, 64, 64}/256</c> 4095 </texttable> 4096 4097 </section> 4098 4099 <section anchor="silk_excitation" toc="include" title="Excitation"> 4100 <t> 4101 SILK codes the excitation using a modified version of the Pyramid Vector 4102 Quantization (PVQ) codebook <xref target="PVQ"/>. 4103 The PVQ codebook is designed for Laplace-distributed values and consists of all 4104 sums of K signed, unit pulses in a vector of dimension N, where two pulses at 4105 the same position are required to have the same sign. 4106 Thus the codebook includes all integer codevectors y of dimension N that 4107 satisfy 4108 <figure align="center"> 4109 <artwork align="center"><![CDATA[ 4110 N-1 4111 __ 4112 \ abs(y[j]) = K . 4113 /_ 4114 j=0 4115 ]]></artwork> 4116 </figure> 4117 Unlike regular PVQ, SILK uses a variable-length, rather than fixed-length, 4118 encoding. 4119 This encoding is better suited to the more Gaussian-like distribution of the 4120 coefficient magnitudes and the non-uniform distribution of their signs (caused 4121 by the quantization offset described below). 4122 SILK also handles large codebooks by coding the least significant bits (LSBs) 4123 of each coefficient directly. 4124 This adds a small coding efficiency loss, but greatly reduces the computation 4125 time and ROM size required for decoding, as implemented in 4126 silk_decode_pulses() (decode_pulses.c). 4127 </t> 4128 4129 <t> 4130 SILK fixes the dimension of the codebook to N = 16. 4131 The excitation is made up of a number of "shell blocks", each 16 samples in 4132 size. 4133 <xref target="silk_shell_block_table"/> lists the number of shell blocks 4134 required for a SILK frame for each possible audio bandwidth and frame size. 4135 10 ms MB frames nominally contain 120 samples (10 ms at 4136 12 kHz), which is not a multiple of 16. 4137 This is handled by coding 8 shell blocks (128 samples) and discarding the final 4138 8 samples of the last block. 4139 The decoder contains no special case that prevents an encoder from placing 4140 pulses in these samples, and they must be correctly parsed from the bitstream 4141 if present, but they are otherwise ignored. 4142 </t> 4143 4144 <texttable anchor="silk_shell_block_table" 4145 title="Number of Shell Blocks Per SILK Frame"> 4146 <ttcol>Audio Bandwidth</ttcol> 4147 <ttcol>Frame Size</ttcol> 4148 <ttcol align="right">Number of Shell Blocks</ttcol> 4149 <c>NB</c> <c>10 ms</c> <c>5</c> 4150 <c>MB</c> <c>10 ms</c> <c>8</c> 4151 <c>WB</c> <c>10 ms</c> <c>10</c> 4152 <c>NB</c> <c>20 ms</c> <c>10</c> 4153 <c>MB</c> <c>20 ms</c> <c>15</c> 4154 <c>WB</c> <c>20 ms</c> <c>20</c> 4155 </texttable> 4156 4157 <section anchor="silk_rate_level" title="Rate Level"> 4158 <t> 4159 The first symbol in the excitation is a "rate level", which is an index from 0 4160 to 8, inclusive, coded using the PDF in <xref target="silk_rate_level_pdfs"/> 4161 corresponding to the signal type of the current frame (from 4162 <xref target="silk_frame_type"/>). 4163 The rate level selects the PDF used to decode the number of pulses in 4164 the individual shell blocks. 4165 It does not directly convey any information about the bitrate or the number of 4166 pulses itself, but merely changes the probability of the symbols in 4167 <xref target="silk_pulse_counts"/>. 4168 Level 0 provides a more efficient encoding at low rates generally, and 4169 level 8 provides a more efficient encoding at high rates generally, 4170 though the most efficient level for a particular SILK frame may depend on the 4171 exact distribution of the coded symbols. 4172 An encoder should, but is not required to, use the most efficient rate level. 4173 </t> 4174 4175 <texttable anchor="silk_rate_level_pdfs" 4176 title="PDFs for the Rate Level"> 4177 <ttcol>Signal Type</ttcol> 4178 <ttcol>PDF</ttcol> 4179 <c>Inactive or Unvoiced</c> 4180 <c>{15, 51, 12, 46, 45, 13, 33, 27, 14}/256</c> 4181 <c>Voiced</c> 4182 <c>{33, 30, 36, 17, 34, 49, 18, 21, 18}/256</c> 4183 </texttable> 4184 4185 </section> 4186 4187 <section anchor="silk_pulse_counts" title="Pulses Per Shell Block"> 4188 <t> 4189 The total number of pulses in each of the shell blocks follows the rate level. 4190 The pulse counts for all of the shell blocks are coded consecutively, before 4191 the content of any of the blocks. 4192 Each block may have anywhere from 0 to 16 pulses, inclusive, coded using the 4193 18-entry PDF in <xref target="silk_pulse_count_pdfs"/> corresponding to the 4194 rate level from <xref target="silk_rate_level"/>. 4195 The special value 17 indicates that this block has one or more additional 4196 LSBs to decode for each coefficient. 4197 If the decoder encounters this value, it decodes another value for the actual 4198 pulse count of the block, but uses the PDF corresponding to the special rate 4199 level 9 instead of the normal rate level. 4200 This process repeats until the decoder reads a value less than 17, and it then 4201 sets the number of extra LSBs used to the number of 17's decoded for that 4202 block. 4203 If it reads the value 17 ten times, then the next iteration uses the special 4204 rate level 10 instead of 9. 4205 The probability of decoding a 17 when using the PDF for rate level 10 is 4206 zero, ensuring that the number of LSBs for a block will not exceed 10. 4207 The cumulative distribution for rate level 10 is just a shifted version of 4208 that for 9 and thus does not require any additional storage. 4209 </t> 4210 4211 <texttable anchor="silk_pulse_count_pdfs" 4212 title="PDFs for the Pulse Count"> 4213 <ttcol>Rate Level</ttcol> 4214 <ttcol>PDF</ttcol> 4215 <c>0</c> 4216 <c>{131, 74, 25, 8, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}/256</c> 4217 <c>1</c> 4218 <c>{58, 93, 60, 23, 7, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}/256</c> 4219 <c>2</c> 4220 <c>{43, 51, 46, 33, 24, 16, 11, 8, 6, 3, 3, 3, 2, 1, 1, 2, 1, 2}/256</c> 4221 <c>3</c> 4222 <c>{17, 52, 71, 57, 31, 12, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}/256</c> 4223 <c>4</c> 4224 <c>{6, 21, 41, 53, 49, 35, 21, 11, 6, 3, 2, 2, 1, 1, 1, 1, 1, 1}/256</c> 4225 <c>5</c> 4226 <c>{7, 14, 22, 28, 29, 28, 25, 20, 17, 13, 11, 9, 7, 5, 4, 4, 3, 10}/256</c> 4227 <c>6</c> 4228 <c>{2, 5, 14, 29, 42, 46, 41, 31, 19, 11, 6, 3, 2, 1, 1, 1, 1, 1}/256</c> 4229 <c>7</c> 4230 <c>{1, 2, 4, 10, 19, 29, 35, 37, 34, 28, 20, 14, 8, 5, 4, 2, 2, 2}/256</c> 4231 <c>8</c> 4232 <c>{1, 2, 2, 5, 9, 14, 20, 24, 27, 28, 26, 23, 20, 15, 11, 8, 6, 15}/256</c> 4233 <c>9</c> 4234 <c>{1, 1, 1, 6, 27, 58, 56, 39, 25, 14, 10, 6, 3, 3, 2, 1, 1, 2}/256</c> 4235 <c>10</c> 4236 <c>{2, 1, 6, 27, 58, 56, 39, 25, 14, 10, 6, 3, 3, 2, 1, 1, 2, 0}/256</c> 4237 </texttable> 4238 4239 </section> 4240 4241 <section anchor="silk_pulse_locations" title="Pulse Location Decoding"> 4242 <t> 4243 The locations of the pulses in each shell block follow the pulse counts, 4244 as decoded by silk_shell_decoder() (shell_coder.c). 4245 As with the pulse counts, these locations are coded for all the shell blocks 4246 before any of the remaining information for each block. 4247 Unlike many other codecs, SILK places no restriction on the distribution of 4248 pulses within a shell block. 4249 All of the pulses may be placed in a single location, or each one in a unique 4250 location, or anything in between. 4251 </t> 4252 4253 <t> 4254 The location of pulses is coded by recursively partitioning each block into 4255 halves, and coding how many pulses fall on the left side of the split. 4256 All remaining pulses must fall on the right side of the split. 4257 The process then recurses into the left half, and after that returns, the 4258 right half (preorder traversal). 4259 The PDF to use is chosen by the size of the current partition (16, 8, 4, or 2) 4260 and the number of pulses in the partition (1 to 16, inclusive). 4261 Tables <xref format="counter" target="silk_shell_code3_pdfs"/> 4262 through <xref format="counter" target="silk_shell_code0_pdfs"/> list the 4263 PDFs used for each partition size and pulse count. 4264 This process skips partitions without any pulses, i.e., where the initial pulse 4265 count from <xref target="silk_pulse_counts"/> was zero, or where the split in 4266 the prior level indicated that all of the pulses fell on the other side. 4267 These partitions have nothing to code, so they require no PDF. 4268 </t> 4269 4270 <texttable anchor="silk_shell_code3_pdfs" 4271 title="PDFs for Pulse Count Split, 16 Sample Partitions"> 4272 <ttcol>Pulse Count</ttcol> 4273 <ttcol>PDF</ttcol> 4274 <c>1</c> <c>{126, 130}/256</c> 4275 <c>2</c> <c>{56, 142, 58}/256</c> 4276 <c>3</c> <c>{25, 101, 104, 26}/256</c> 4277 <c>4</c> <c>{12, 60, 108, 64, 12}/256</c> 4278 <c>5</c> <c>{7, 35, 84, 87, 37, 6}/256</c> 4279 <c>6</c> <c>{4, 20, 59, 86, 63, 21, 3}/256</c> 4280 <c>7</c> <c>{3, 12, 38, 72, 75, 42, 12, 2}/256</c> 4281 <c>8</c> <c>{2, 8, 25, 54, 73, 59, 27, 7, 1}/256</c> 4282 <c>9</c> <c>{2, 5, 17, 39, 63, 65, 42, 18, 4, 1}/256</c> 4283 <c>10</c> <c>{1, 4, 12, 28, 49, 63, 54, 30, 11, 3, 1}/256</c> 4284 <c>11</c> <c>{1, 4, 8, 20, 37, 55, 57, 41, 22, 8, 2, 1}/256</c> 4285 <c>12</c> <c>{1, 3, 7, 15, 28, 44, 53, 48, 33, 16, 6, 1, 1}/256</c> 4286 <c>13</c> <c>{1, 2, 6, 12, 21, 35, 47, 48, 40, 25, 12, 5, 1, 1}/256</c> 4287 <c>14</c> <c>{1, 1, 4, 10, 17, 27, 37, 47, 43, 33, 21, 9, 4, 1, 1}/256</c> 4288 <c>15</c> <c>{1, 1, 1, 8, 14, 22, 33, 40, 43, 38, 28, 16, 8, 1, 1, 1}/256</c> 4289 <c>16</c> <c>{1, 1, 1, 1, 13, 18, 27, 36, 41, 41, 34, 24, 14, 1, 1, 1, 1}/256</c> 4290 </texttable> 4291 4292 <texttable anchor="silk_shell_code2_pdfs" 4293 title="PDFs for Pulse Count Split, 8 Sample Partitions"> 4294 <ttcol>Pulse Count</ttcol> 4295 <ttcol>PDF</ttcol> 4296 <c>1</c> <c>{127, 129}/256</c> 4297 <c>2</c> <c>{53, 149, 54}/256</c> 4298 <c>3</c> <c>{22, 105, 106, 23}/256</c> 4299 <c>4</c> <c>{11, 61, 111, 63, 10}/256</c> 4300 <c>5</c> <c>{6, 35, 86, 88, 36, 5}/256</c> 4301 <c>6</c> <c>{4, 20, 59, 87, 62, 21, 3}/256</c> 4302 <c>7</c> <c>{3, 13, 40, 71, 73, 41, 13, 2}/256</c> 4303 <c>8</c> <c>{3, 9, 27, 53, 70, 56, 28, 9, 1}/256</c> 4304 <c>9</c> <c>{3, 8, 19, 37, 57, 61, 44, 20, 6, 1}/256</c> 4305 <c>10</c> <c>{3, 7, 15, 28, 44, 54, 49, 33, 17, 5, 1}/256</c> 4306 <c>11</c> <c>{1, 7, 13, 22, 34, 46, 48, 38, 28, 14, 4, 1}/256</c> 4307 <c>12</c> <c>{1, 1, 11, 22, 27, 35, 42, 47, 33, 25, 10, 1, 1}/256</c> 4308 <c>13</c> <c>{1, 1, 6, 14, 26, 37, 43, 43, 37, 26, 14, 6, 1, 1}/256</c> 4309 <c>14</c> <c>{1, 1, 4, 10, 20, 31, 40, 42, 40, 31, 20, 10, 4, 1, 1}/256</c> 4310 <c>15</c> <c>{1, 1, 3, 8, 16, 26, 35, 38, 38, 35, 26, 16, 8, 3, 1, 1}/256</c> 4311 <c>16</c> <c>{1, 1, 2, 6, 12, 21, 30, 36, 38, 36, 30, 21, 12, 6, 2, 1, 1}/256</c> 4312 </texttable> 4313 4314 <texttable anchor="silk_shell_code1_pdfs" 4315 title="PDFs for Pulse Count Split, 4 Sample Partitions"> 4316 <ttcol>Pulse Count</ttcol> 4317 <ttcol>PDF</ttcol> 4318 <c>1</c> <c>{127, 129}/256</c> 4319 <c>2</c> <c>{49, 157, 50}/256</c> 4320 <c>3</c> <c>{20, 107, 109, 20}/256</c> 4321 <c>4</c> <c>{11, 60, 113, 62, 10}/256</c> 4322 <c>5</c> <c>{7, 36, 84, 87, 36, 6}/256</c> 4323 <c>6</c> <c>{6, 24, 57, 82, 60, 23, 4}/256</c> 4324 <c>7</c> <c>{5, 18, 39, 64, 68, 42, 16, 4}/256</c> 4325 <c>8</c> <c>{6, 14, 29, 47, 61, 52, 30, 14, 3}/256</c> 4326 <c>9</c> <c>{1, 15, 23, 35, 51, 50, 40, 30, 10, 1}/256</c> 4327 <c>10</c> <c>{1, 1, 21, 32, 42, 52, 46, 41, 18, 1, 1}/256</c> 4328 <c>11</c> <c>{1, 6, 16, 27, 36, 42, 42, 36, 27, 16, 6, 1}/256</c> 4329 <c>12</c> <c>{1, 5, 12, 21, 31, 38, 40, 38, 31, 21, 12, 5, 1}/256</c> 4330 <c>13</c> <c>{1, 3, 9, 17, 26, 34, 38, 38, 34, 26, 17, 9, 3, 1}/256</c> 4331 <c>14</c> <c>{1, 3, 7, 14, 22, 29, 34, 36, 34, 29, 22, 14, 7, 3, 1}/256</c> 4332 <c>15</c> <c>{1, 2, 5, 11, 18, 25, 31, 35, 35, 31, 25, 18, 11, 5, 2, 1}/256</c> 4333 <c>16</c> <c>{1, 1, 4, 9, 15, 21, 28, 32, 34, 32, 28, 21, 15, 9, 4, 1, 1}/256</c> 4334 </texttable> 4335 4336 <texttable anchor="silk_shell_code0_pdfs" 4337 title="PDFs for Pulse Count Split, 2 Sample Partitions"> 4338 <ttcol>Pulse Count</ttcol> 4339 <ttcol>PDF</ttcol> 4340 <c>1</c> <c>{128, 128}/256</c> 4341 <c>2</c> <c>{42, 172, 42}/256</c> 4342 <c>3</c> <c>{21, 107, 107, 21}/256</c> 4343 <c>4</c> <c>{12, 60, 112, 61, 11}/256</c> 4344 <c>5</c> <c>{8, 34, 86, 86, 35, 7}/256</c> 4345 <c>6</c> <c>{8, 23, 55, 90, 55, 20, 5}/256</c> 4346 <c>7</c> <c>{5, 15, 38, 72, 72, 36, 15, 3}/256</c> 4347 <c>8</c> <c>{6, 12, 27, 52, 77, 47, 20, 10, 5}/256</c> 4348 <c>9</c> <c>{6, 19, 28, 35, 40, 40, 35, 28, 19, 6}/256</c> 4349 <c>10</c> <c>{4, 14, 22, 31, 37, 40, 37, 31, 22, 14, 4}/256</c> 4350 <c>11</c> <c>{3, 10, 18, 26, 33, 38, 38, 33, 26, 18, 10, 3}/256</c> 4351 <c>12</c> <c>{2, 8, 13, 21, 29, 36, 38, 36, 29, 21, 13, 8, 2}/256</c> 4352 <c>13</c> <c>{1, 5, 10, 17, 25, 32, 38, 38, 32, 25, 17, 10, 5, 1}/256</c> 4353 <c>14</c> <c>{1, 4, 7, 13, 21, 29, 35, 36, 35, 29, 21, 13, 7, 4, 1}/256</c> 4354 <c>15</c> <c>{1, 2, 5, 10, 17, 25, 32, 36, 36, 32, 25, 17, 10, 5, 2, 1}/256</c> 4355 <c>16</c> <c>{1, 2, 4, 7, 13, 21, 28, 34, 36, 34, 28, 21, 13, 7, 4, 2, 1}/256</c> 4356 </texttable> 4357 4358 </section> 4359 4360 <section anchor="silk_shell_lsb" title="LSB Decoding"> 4361 <t> 4362 After the decoder reads the pulse locations for all blocks, it reads the LSBs 4363 (if any) for each block in turn. 4364 Inside each block, it reads all the LSBs for each coefficient in turn, even 4365 those where no pulses were allocated, before proceeding to the next one. 4366 For 10 ms MB frames, it reads LSBs even for the extra 8 samples in 4367 the last block. 4368 The LSBs are coded from most significant to least significant, and they all use 4369 the PDF in <xref target="silk_shell_lsb_pdf"/>. 4370 </t> 4371 4372 <texttable anchor="silk_shell_lsb_pdf" title="PDF for Excitation LSBs"> 4373 <ttcol>PDF</ttcol> 4374 <c>{136, 120}/256</c> 4375 </texttable> 4376 4377 <t> 4378 The number of LSBs read for each coefficient in a block is determined in 4379 <xref target="silk_pulse_counts"/>. 4380 The magnitude of the coefficient is initially equal to the number of pulses 4381 placed at that location in <xref target="silk_pulse_locations"/>. 4382 As each LSB is decoded, the magnitude is doubled, and then the value of the LSB 4383 added to it, to obtain an updated magnitude. 4384 </t> 4385 </section> 4386 4387 <section anchor="silk_signs" title="Sign Decoding"> 4388 <t> 4389 After decoding the pulse locations and the LSBs, the decoder knows the 4390 magnitude of each coefficient in the excitation. 4391 It then decodes a sign for all coefficients with a non-zero magnitude, using 4392 one of the PDFs from <xref target="silk_sign_pdfs"/>. 4393 If the value decoded is 0, then the coefficient magnitude is negated. 4394 Otherwise, it remains positive. 4395 </t> 4396 4397 <t> 4398 The decoder chooses the PDF for the sign based on the signal type and 4399 quantization offset type (from <xref target="silk_frame_type"/>) and the 4400 number of pulses in the block (from <xref target="silk_pulse_counts"/>). 4401 The number of pulses in the block does not take into account any LSBs. 4402 Most PDFs are skewed towards negative signs because of the quantization offset, 4403 but the PDFs for zero pulses are highly skewed towards positive signs. 4404 If a block contains many positive coefficients, it is sometimes beneficial to 4405 code it solely using LSBs (i.e., with zero pulses), since the encoder may be 4406 able to save enough bits on the signs to justify the less efficient 4407 coefficient magnitude encoding. 4408 </t> 4409 4410 <texttable anchor="silk_sign_pdfs" 4411 title="PDFs for Excitation Signs"> 4412 <ttcol>Signal Type</ttcol> 4413 <ttcol>Quantization Offset Type</ttcol> 4414 <ttcol>Pulse Count</ttcol> 4415 <ttcol>PDF</ttcol> 4416 <c>Inactive</c> <c>Low</c> <c>0</c> <c>{2, 254}/256</c> 4417 <c>Inactive</c> <c>Low</c> <c>1</c> <c>{207, 49}/256</c> 4418 <c>Inactive</c> <c>Low</c> <c>2</c> <c>{189, 67}/256</c> 4419 <c>Inactive</c> <c>Low</c> <c>3</c> <c>{179, 77}/256</c> 4420 <c>Inactive</c> <c>Low</c> <c>4</c> <c>{174, 82}/256</c> 4421 <c>Inactive</c> <c>Low</c> <c>5</c> <c>{163, 93}/256</c> 4422 <c>Inactive</c> <c>Low</c> <c>6 or more</c> <c>{157, 99}/256</c> 4423 <c>Inactive</c> <c>High</c> <c>0</c> <c>{58, 198}/256</c> 4424 <c>Inactive</c> <c>High</c> <c>1</c> <c>{245, 11}/256</c> 4425 <c>Inactive</c> <c>High</c> <c>2</c> <c>{238, 18}/256</c> 4426 <c>Inactive</c> <c>High</c> <c>3</c> <c>{232, 24}/256</c> 4427 <c>Inactive</c> <c>High</c> <c>4</c> <c>{225, 31}/256</c> 4428 <c>Inactive</c> <c>High</c> <c>5</c> <c>{220, 36}/256</c> 4429 <c>Inactive</c> <c>High</c> <c>6 or more</c> <c>{211, 45}/256</c> 4430 <c>Unvoiced</c> <c>Low</c> <c>0</c> <c>{1, 255}/256</c> 4431 <c>Unvoiced</c> <c>Low</c> <c>1</c> <c>{210, 46}/256</c> 4432 <c>Unvoiced</c> <c>Low</c> <c>2</c> <c>{190, 66}/256</c> 4433 <c>Unvoiced</c> <c>Low</c> <c>3</c> <c>{178, 78}/256</c> 4434 <c>Unvoiced</c> <c>Low</c> <c>4</c> <c>{169, 87}/256</c> 4435 <c>Unvoiced</c> <c>Low</c> <c>5</c> <c>{162, 94}/256</c> 4436 <c>Unvoiced</c> <c>Low</c> <c>6 or more</c> <c>{152, 104}/256</c> 4437 <c>Unvoiced</c> <c>High</c> <c>0</c> <c>{48, 208}/256</c> 4438 <c>Unvoiced</c> <c>High</c> <c>1</c> <c>{242, 14}/256</c> 4439 <c>Unvoiced</c> <c>High</c> <c>2</c> <c>{235, 21}/256</c> 4440 <c>Unvoiced</c> <c>High</c> <c>3</c> <c>{224, 32}/256</c> 4441 <c>Unvoiced</c> <c>High</c> <c>4</c> <c>{214, 42}/256</c> 4442 <c>Unvoiced</c> <c>High</c> <c>5</c> <c>{205, 51}/256</c> 4443 <c>Unvoiced</c> <c>High</c> <c>6 or more</c> <c>{190, 66}/256</c> 4444 <c>Voiced</c> <c>Low</c> <c>0</c> <c>{1, 255}/256</c> 4445 <c>Voiced</c> <c>Low</c> <c>1</c> <c>{162, 94}/256</c> 4446 <c>Voiced</c> <c>Low</c> <c>2</c> <c>{152, 104}/256</c> 4447 <c>Voiced</c> <c>Low</c> <c>3</c> <c>{147, 109}/256</c> 4448 <c>Voiced</c> <c>Low</c> <c>4</c> <c>{144, 112}/256</c> 4449 <c>Voiced</c> <c>Low</c> <c>5</c> <c>{141, 115}/256</c> 4450 <c>Voiced</c> <c>Low</c> <c>6 or more</c> <c>{138, 118}/256</c> 4451 <c>Voiced</c> <c>High</c> <c>0</c> <c>{8, 248}/256</c> 4452 <c>Voiced</c> <c>High</c> <c>1</c> <c>{203, 53}/256</c> 4453 <c>Voiced</c> <c>High</c> <c>2</c> <c>{187, 69}/256</c> 4454 <c>Voiced</c> <c>High</c> <c>3</c> <c>{176, 80}/256</c> 4455 <c>Voiced</c> <c>High</c> <c>4</c> <c>{168, 88}/256</c> 4456 <c>Voiced</c> <c>High</c> <c>5</c> <c>{161, 95}/256</c> 4457 <c>Voiced</c> <c>High</c> <c>6 or more</c> <c>{154, 102}/256</c> 4458 </texttable> 4459 4460 </section> 4461 4462 <section anchor="silk_excitation_reconstruction" 4463 title="Reconstructing the Excitation"> 4464 4465 <t> 4466 After the signs have been read, there is enough information to reconstruct the 4467 complete excitation signal. 4468 This requires adding a constant quantization offset to each non-zero sample, 4469 and then pseudorandomly inverting and offsetting every sample. 4470 The constant quantization offset varies depending on the signal type and 4471 quantization offset type (see <xref target="silk_frame_type"/>). 4472 </t> 4473 4474 <texttable anchor="silk_quantization_offsets" 4475 title="Excitation Quantization Offsets"> 4476 <ttcol align="left">Signal Type</ttcol> 4477 <ttcol align="left">Quantization Offset Type</ttcol> 4478 <ttcol align="right">Quantization Offset (Q23)</ttcol> 4479 <c>Inactive</c> <c>Low</c> <c>25</c> 4480 <c>Inactive</c> <c>High</c> <c>60</c> 4481 <c>Unvoiced</c> <c>Low</c> <c>25</c> 4482 <c>Unvoiced</c> <c>High</c> <c>60</c> 4483 <c>Voiced</c> <c>Low</c> <c>8</c> 4484 <c>Voiced</c> <c>High</c> <c>25</c> 4485 </texttable> 4486 4487 <t> 4488 Let e_raw[i] be the raw excitation value at position i, with a magnitude 4489 composed of the pulses at that location (see 4490 <xref target="silk_pulse_locations"/>) combined with any additional LSBs (see 4491 <xref target="silk_shell_lsb"/>), and with the corresponding sign decoded in 4492 <xref target="silk_signs"/>. 4493 Additionally, let seed be the current pseudorandom seed, which is initialized 4494 to the value decoded from <xref target="silk_seed"/> for the first sample in 4495 the current SILK frame, and updated for each subsequent sample according to 4496 the procedure below. 4497 Finally, let offset_Q23 be the quantization offset from 4498 <xref target="silk_quantization_offsets"/>. 4499 Then the following procedure produces the final reconstructed excitation value, 4500 e_Q23[i]: 4501 <figure align="center"> 4502 <artwork align="center"><![CDATA[ 4503 e_Q23[i] = (e_raw[i] << 8) - sign(e_raw[i])*20 + offset_Q23; 4504 seed = (196314165*seed + 907633515) & 0xFFFFFFFF; 4505 e_Q23[i] = (seed & 0x80000000) ? -e_Q23[i] : e_Q23[i]; 4506 seed = (seed + e_raw[i]) & 0xFFFFFFFF; 4507 ]]></artwork> 4508 </figure> 4509 When e_raw[i] is zero, sign() returns 0 by the definition in 4510 <xref target="sign"/>, so the factor of 20 does not get added. 4511 The final e_Q23[i] value may require more than 16 bits per sample, but will not 4512 require more than 23, including the sign. 4513 </t> 4514 4515 </section> 4516 4517 </section> 4518 4519 <section anchor="silk_frame_reconstruction" toc="include" 4520 title="SILK Frame Reconstruction"> 4521 4522 <t> 4523 The remainder of the reconstruction process for the frame does not need to be 4524 bit-exact, as small errors should only introduce proportionally small 4525 distortions. 4526 Although the reference implementation only includes a fixed-point version of 4527 the remaining steps, this section describes them in terms of a floating-point 4528 version for simplicity. 4529 This produces a signal with a nominal range of -1.0 to 1.0. 4530 </t> 4531 4532 <t> 4533 silk_decode_core() (decode_core.c) contains the code for the main 4534 reconstruction process. 4535 It proceeds subframe-by-subframe, since quantization gains, LTP parameters, and 4536 (in 20 ms SILK frames) LPC coefficients can vary from one to the 4537 next. 4538 </t> 4539 4540 <t> 4541 Let a_Q12[k] be the LPC coefficients for the current subframe. 4542 If this is the first or second subframe of a 20 ms SILK frame and the LSF 4543 interpolation factor, w_Q2 (see <xref target="silk_nlsf_interpolation"/>), is 4544 less than 4, then these correspond to the final LPC coefficients produced by 4545 <xref target="silk_lpc_gain_limit"/> from the interpolated LSF coefficients, 4546 n1_Q15[k] (computed in <xref target="silk_nlsf_interpolation"/>). 4547 Otherwise, they correspond to the final LPC coefficients produced from the 4548 uninterpolated LSF coefficients for the current frame, n2_Q15[k]. 4549 </t> 4550 4551 <t> 4552 Also, let n be the number of samples in a subframe (40 for NB, 60 for MB, and 4553 80 for WB), s be the index of the current subframe in this SILK frame (0 or 1 4554 for 10 ms frames, or 0 to 3 for 20 ms frames), and j be the index of 4555 the first sample in the residual corresponding to the current subframe. 4556 </t> 4557 4558 <section anchor="silk_ltp_synthesis" title="LTP Synthesis"> 4559 <t> 4560 Voiced SILK frames (see <xref target="silk_frame_type"/>) pass the excitation 4561 through an LTP filter using the parameters decoded in 4562 <xref target="silk_ltp_params"/> to produce an LPC residual. 4563 The LTP filter requires LPC residual values from before the current subframe as 4564 input. 4565 However, since the LPC coefficients may have changed, it obtains this residual 4566 by "rewhitening" the corresponding output signal using the LPC coefficients 4567 from the current subframe. 4568 Let out[i] for 4569 (j - pitch_lags[s] - d_LPC - 2) <= i < j 4570 be the fully reconstructed output signal from the last 4571 (pitch_lags[s] + d_LPC + 2) samples of previous subframes 4572 (see <xref target="silk_lpc_synthesis"/>), where pitch_lags[s] is the pitch 4573 lag for the current subframe from <xref target="silk_ltp_lags"/>. 4574 During reconstruction of the first subframe for this channel after either 4575 <list style="symbols"> 4576 <t>An uncoded regular SILK frame (if this is the side channel), or</t> 4577 <t>A decoder reset (see <xref target="decoder-reset"/>),</t> 4578 </list> 4579 out[] is rewhitened into an LPC residual, 4580 res[i], via 4581 <figure align="center"> 4582 <artwork align="center"><![CDATA[ 4583 4.0*LTP_scale_Q14 4584 res[i] = ----------------- * clamp(-1.0, 4585 gain_Q16[s] 4586 4587 d_LPC-1 4588 __ a_Q12[k] 4589 out[i] - \ out[i-k-1] * --------, 1.0) . 4590 /_ 4096.0 4591 k=0 4592 ]]></artwork> 4593 </figure> 4594 This requires storage to buffer up to 306 values of out[i] from previous 4595 subframes. 4596 This corresponds to WB with a maximum pitch lag of 4597 18 ms * 16 kHz samples, plus 16 samples for d_LPC, plus 2 4598 samples for the width of the LTP filter. 4599 </t> 4600 4601 <t> 4602 Let e_Q23[i] for j <= i < (j + n) be the 4603 excitation for the current subframe, and b_Q7[k] for 4604 0 <= k < 5 be the coefficients of the LTP filter 4605 taken from the codebook entry in one of 4606 Tables <xref format="counter" target="silk_ltp_filter_coeffs0"/> 4607 through <xref format="counter" target="silk_ltp_filter_coeffs2"/> 4608 corresponding to the index decoded for the current subframe in 4609 <xref target="silk_ltp_filter"/>. 4610 Then for i such that j <= i < (j + n), 4611 the LPC residual is 4612 <figure align="center"> 4613 <artwork align="center"><![CDATA[ 4614 4 4615 e_Q23[i] __ b_Q7[k] 4616 res[i] = --------- + \ res[i - pitch_lags[s] + 2 - k] * ------- . 4617 2.0**23 /_ 128.0 4618 k=0 4619 ]]></artwork> 4620 </figure> 4621 </t> 4622 4623 <t> 4624 For unvoiced frames, the LPC residual for 4625 j <= i < (j + n) is simply a normalized 4626 copy of the excitation signal, i.e., 4627 <figure align="center"> 4628 <artwork align="center"><![CDATA[ 4629 e_Q23[i] 4630 res[i] = --------- 4631 2.0**23 4632 ]]></artwork> 4633 </figure> 4634 </t> 4635 </section> 4636 4637 <section anchor="silk_lpc_synthesis" title="LPC Synthesis"> 4638 <t> 4639 LPC synthesis uses the short-term LPC filter to predict the next output 4640 coefficient. 4641 For i such that (j - d_LPC) <= i < j, let 4642 lpc[i] be the result of LPC synthesis from the last d_LPC samples of the 4643 previous subframe, or zeros in the first subframe for this channel after 4644 either 4645 <list style="symbols"> 4646 <t>An uncoded regular SILK frame (if this is the side channel), or</t> 4647 <t>A decoder reset (see <xref target="decoder-reset"/>).</t> 4648 </list> 4649 Then for i such that j <= i < (j + n), the 4650 result of LPC synthesis for the current subframe is 4651 <figure align="center"> 4652 <artwork align="center"><![CDATA[ 4653 d_LPC-1 4654 gain_Q16[i] __ a_Q12[k] 4655 lpc[i] = ----------- * res[i] + \ lpc[i-k-1] * -------- . 4656 65536.0 /_ 4096.0 4657 k=0 4658 ]]></artwork> 4659 </figure> 4660 The decoder saves the final d_LPC values, i.e., lpc[i] such that 4661 (j + n - d_LPC) <= i < (j + n), 4662 to feed into the LPC synthesis of the next subframe. 4663 This requires storage for up to 16 values of lpc[i] (for WB frames). 4664 </t> 4665 4666 <t> 4667 Then, the signal is clamped into the final nominal range: 4668 <figure align="center"> 4669 <artwork align="center"><![CDATA[ 4670 out[i] = clamp(-1.0, lpc[i], 1.0) . 4671 ]]></artwork> 4672 </figure> 4673 This clamping occurs entirely after the LPC synthesis filter has run. 4674 The decoder saves the unclamped values, lpc[i], to feed into the LPC filter for 4675 the next subframe, but saves the clamped values, out[i], for rewhitening in 4676 voiced frames. 4677 </t> 4678 </section> 4679 4680 </section> 4681 4682 </section> 4683 4684 <section anchor="silk_stereo_unmixing" title="Stereo Unmixing"> 4685 <t> 4686 For stereo streams, after decoding a frame from each channel, the decoder must 4687 convert the mid-side (MS) representation into a left-right (LR) 4688 representation. 4689 The function silk_stereo_MS_to_LR (stereo_MS_to_LR.c) implements this process. 4690 In it, the decoder predicts the side channel using a) a simple low-passed 4691 version of the mid channel, and b) the unfiltered mid channel, using the 4692 prediction weights decoded in <xref target="silk_stereo_pred"/>. 4693 This simple low-pass filter imposes a one-sample delay, and the unfiltered 4694 mid channel is also delayed by one sample. 4695 In order to allow seamless switching between stereo and mono, mono streams must 4696 also impose the same one-sample delay. 4697 The encoder requires an additional one-sample delay for both mono and stereo 4698 streams, though an encoder may omit the delay for mono if it knows it will 4699 never switch to stereo. 4700 </t> 4701 4702 <t> 4703 The unmixing process operates in two phases. 4704 The first phase lasts for 8 ms, during which it interpolates the 4705 prediction weights from the previous frame, prev_w0_Q13 and prev_w1_Q13, to 4706 the values for the current frame, w0_Q13 and w1_Q13. 4707 The second phase simply uses these weights for the remainder of the frame. 4708 </t> 4709 4710 <t> 4711 Let mid[i] and side[i] be the contents of out[i] (from 4712 <xref target="silk_lpc_synthesis"/>) for the current mid and side channels, 4713 respectively, and let left[i] and right[i] be the corresponding stereo output 4714 channels. 4715 If the side channel is not coded (see <xref target="silk_mid_only_flag"/>), 4716 then side[i] is set to zero. 4717 Also let j be defined as in <xref target="silk_frame_reconstruction"/>, n1 be 4718 the number of samples in phase 1 (64 for NB, 96 for MB, and 128 for WB), 4719 and n2 be the total number of samples in the frame. 4720 Then for i such that j <= i < (j + n2), 4721 the left and right channel output is 4722 <figure align="center"> 4723 <artwork align="center"><![CDATA[ 4724 prev_w0_Q13 (w0_Q13 - prev_w0_Q13) 4725 w0 = ----------- + min(i - j, n1)*---------------------- , 4726 8192.0 8192.0*n1 4727 4728 prev_w1_Q13 (w1_Q13 - prev_w1_Q13) 4729 w1 = ----------- + min(i - j, n1)*---------------------- , 4730 8192.0 8192.0*n1 4731 4732 mid[i-2] + 2*mid[i-1] + mid[i] 4733 p0 = ------------------------------ , 4734 4.0 4735 4736 left[i] = clamp(-1.0, (1 + w1)*mid[i-1] + side[i-1] + w0*p0, 1.0) , 4737 4738 right[i] = clamp(-1.0, (1 - w1)*mid[i-1] - side[i-1] - w0*p0, 1.0) . 4739 ]]></artwork> 4740 </figure> 4741 These formulas require two samples prior to index j, the start of the 4742 frame, for the mid channel, and one prior sample for the side channel. 4743 For the first frame after a decoder reset, zeros are used instead. 4744 </t> 4745 4746 </section> 4747 4748 <section title="Resampling"> 4749 <t> 4750 After stereo unmixing (if any), the decoder applies resampling to convert the 4751 decoded SILK output to the sample rate desired by the application. 4752 This is necessary when decoding a Hybrid frame at SWB or FB sample rates, or 4753 whenever the decoder wants the output at a different sample rate than the 4754 internal SILK sampling rate (e.g., to allow a constant sample rate when the 4755 audio bandwidth changes, or to allow mixing with audio from other 4756 applications). 4757 The resampler itself is non-normative, and a decoder can use any method it 4758 wants to perform the resampling. 4759 </t> 4760 4761 <t> 4762 However, a minimum amount of delay is imposed to allow the resampler to 4763 operate, and this delay is normative, so that the corresponding delay can be 4764 applied to the MDCT layer in the encoder. 4765 A decoder is always free to use a resampler which requires more delay than 4766 allowed for here (e.g., to improve quality), but it must then delay the output 4767 of the MDCT layer by this extra amount. 4768 Keeping as much delay as possible on the encoder side allows an encoder which 4769 knows it will never use any of the SILK or Hybrid modes to skip this delay. 4770 By contrast, if it were all applied by the decoder, then a decoder which 4771 processes audio in fixed-size blocks would be forced to delay the output of 4772 CELT frames just in case of a later switch to a SILK or Hybrid mode. 4773 </t> 4774 4775 <t> 4776 <xref target="silk_resampler_delay_alloc"/> gives the maximum resampler delay 4777 in samples at 48 kHz for each SILK audio bandwidth. 4778 Because the actual output rate may not be 48 kHz, it may not be possible 4779 to achieve exactly these delays while using a whole number of input or output 4780 samples. 4781 The reference implementation is able to resample to any of the supported 4782 output sampling rates (8, 12, 16, 24, or 48 kHz) within or near this 4783 delay constraint. 4784 Some resampling filters (including those used by the reference implementation) 4785 may add a delay that is not an exact integer, or is not linear-phase, and so 4786 cannot be represented by a single delay at all frequencies. 4787 However, such deviations are unlikely to be perceptible, and the comparison 4788 tool described in <xref target="conformance"/> is designed to be relatively 4789 insensitive to them. 4790 The delays listed here are the ones that should be targeted by the encoder. 4791 </t> 4792 4793 <texttable anchor="silk_resampler_delay_alloc" 4794 title="SILK Resampler Delay Allocations"> 4795 <ttcol>Audio Bandwidth</ttcol> 4796 <ttcol>Delay in millisecond</ttcol> 4797 <c>NB</c> <c>0.538</c> 4798 <c>MB</c> <c>0.692</c> 4799 <c>WB</c> <c>0.706</c> 4800 </texttable> 4801 4802 <t> 4803 NB is given a smaller decoder delay allocation than MB and WB to allow a 4804 higher-order filter when resampling to 8 kHz in both the encoder and 4805 decoder. 4806 This implies that the audio content of two SILK frames operating at different 4807 bandwidths are not perfectly aligned in time. 4808 This is not an issue for any transitions described in 4809 <xref target="switching"/>, because they all involve a SILK decoder reset. 4810 When the decoder is reset, any samples remaining in the resampling buffer 4811 are discarded, and the resampler is re-initialized with silence. 4812 </t> 4813 4814 </section> 4815 4816 </section> 4817 4818 4819 <section title="CELT Decoder"> 4820 4821 <t> 4822 The CELT layer of Opus is based on the Modified Discrete Cosine Transform 4823 <xref target='MDCT'/> with partially overlapping windows of 5 to 22.5 ms. 4824 The main principle behind CELT is that the MDCT spectrum is divided into 4825 bands that (roughly) follow the Bark scale, i.e., the scale of the ear's 4826 critical bands <xref target="Zwicker61"/>. The normal CELT layer uses 21 of those bands, though Opus 4827 Custom (see <xref target="opus-custom"/>) may use a different number of bands. 4828 In Hybrid mode, the first 17 bands (up to 8 kHz) are not coded. 4829 A band can contain as little as one MDCT bin per channel, and as many as 176 4830 bins per channel, as detailed in <xref target="celt_band_sizes"/>. 4831 In each band, the gain (energy) is coded separately from 4832 the shape of the spectrum. Coding the gain explicitly makes it easy to 4833 preserve the spectral envelope of the signal. The remaining unit-norm shape 4834 vector is encoded using a Pyramid Vector Quantizer (PVQ) <xref target='PVQ-decoder'/>. 4835 </t> 4836 4837 <texttable anchor="celt_band_sizes" 4838 title="MDCT Bins Per Channel Per Band for Each Frame Size"> 4839 <ttcol>Frame Size:</ttcol> 4840 <ttcol align="right">2.5 ms</ttcol> 4841 <ttcol align="right">5 ms</ttcol> 4842 <ttcol align="right">10 ms</ttcol> 4843 <ttcol align="right">20 ms</ttcol> 4844 <ttcol align="right">Start Frequency</ttcol> 4845 <ttcol align="right">Stop Frequency</ttcol> 4846 <c>Band</c> <c>Bins:</c> <c/> <c/> <c/> <c/> <c/> 4847 <c>0</c> <c>1</c> <c>2</c> <c>4</c> <c>8</c> <c>0 Hz</c> <c>200 Hz</c> 4848 <c>1</c> <c>1</c> <c>2</c> <c>4</c> <c>8</c> <c>200 Hz</c> <c>400 Hz</c> 4849 <c>2</c> <c>1</c> <c>2</c> <c>4</c> <c>8</c> <c>400 Hz</c> <c>600 Hz</c> 4850 <c>3</c> <c>1</c> <c>2</c> <c>4</c> <c>8</c> <c>600 Hz</c> <c>800 Hz</c> 4851 <c>4</c> <c>1</c> <c>2</c> <c>4</c> <c>8</c> <c>800 Hz</c> <c>1000 Hz</c> 4852 <c>5</c> <c>1</c> <c>2</c> <c>4</c> <c>8</c> <c>1000 Hz</c> <c>1200 Hz</c> 4853 <c>6</c> <c>1</c> <c>2</c> <c>4</c> <c>8</c> <c>1200 Hz</c> <c>1400 Hz</c> 4854 <c>7</c> <c>1</c> <c>2</c> <c>4</c> <c>8</c> <c>1400 Hz</c> <c>1600 Hz</c> 4855 <c>8</c> <c>2</c> <c>4</c> <c>8</c> <c>16</c> <c>1600 Hz</c> <c>2000 Hz</c> 4856 <c>9</c> <c>2</c> <c>4</c> <c>8</c> <c>16</c> <c>2000 Hz</c> <c>2400 Hz</c> 4857 <c>10</c> <c>2</c> <c>4</c> <c>8</c> <c>16</c> <c>2400 Hz</c> <c>2800 Hz</c> 4858 <c>11</c> <c>2</c> <c>4</c> <c>8</c> <c>16</c> <c>2800 Hz</c> <c>3200 Hz</c> 4859 <c>12</c> <c>4</c> <c>8</c> <c>16</c> <c>32</c> <c>3200 Hz</c> <c>4000 Hz</c> 4860 <c>13</c> <c>4</c> <c>8</c> <c>16</c> <c>32</c> <c>4000 Hz</c> <c>4800 Hz</c> 4861 <c>14</c> <c>4</c> <c>8</c> <c>16</c> <c>32</c> <c>4800 Hz</c> <c>5600 Hz</c> 4862 <c>15</c> <c>6</c> <c>12</c> <c>24</c> <c>48</c> <c>5600 Hz</c> <c>6800 Hz</c> 4863 <c>16</c> <c>6</c> <c>12</c> <c>24</c> <c>48</c> <c>6800 Hz</c> <c>8000 Hz</c> 4864 <c>17</c> <c>8</c> <c>16</c> <c>32</c> <c>64</c> <c>8000 Hz</c> <c>9600 Hz</c> 4865 <c>18</c> <c>12</c> <c>24</c> <c>48</c> <c>96</c> <c>9600 Hz</c> <c>12000 Hz</c> 4866 <c>19</c> <c>18</c> <c>36</c> <c>72</c> <c>144</c> <c>12000 Hz</c> <c>15600 Hz</c> 4867 <c>20</c> <c>22</c> <c>44</c> <c>88</c> <c>176</c> <c>15600 Hz</c> <c>20000 Hz</c> 4868 </texttable> 4869 4870 <t> 4871 Transients are notoriously difficult for transform codecs to code. 4872 CELT uses two different strategies for them: 4873 <list style="numbers"> 4874 <t>Using multiple smaller MDCTs instead of a single large MDCT, and</t> 4875 <t>Dynamic time-frequency resolution changes (See <xref target='tf-change'/>).</t> 4876 </list> 4877 To improve quality on highly tonal and periodic signals, CELT includes 4878 a prefilter/postfilter combination. The prefilter on the encoder side 4879 attenuates the signal's harmonics. The postfilter on the decoder side 4880 restores the original gain of the harmonics, while shaping the coding noise 4881 to roughly follow the harmonics. Such noise shaping reduces the perception 4882 of the noise. 4883 </t> 4884 4885 <t> 4886 When coding a stereo signal, three coding methods are available: 4887 <list style="symbols"> 4888 <t>mid-side stereo: encodes the mean and the difference of the left and right channels,</t> 4889 <t>intensity stereo: only encodes the mean of the left and right channels (discards the difference),</t> 4890 <t>dual stereo: encodes the left and right channels separately.</t> 4891 </list> 4892 </t> 4893 4894 <t> 4895 An overview of the decoder is given in <xref target="celt-decoder-overview"/>. 4896 </t> 4897 4898 <figure anchor="celt-decoder-overview" title="Structure of the CELT decoder"> 4899 <artwork align="center"><![CDATA[ 4900 +---------+ 4901 | Coarse | 4902 +->| decoder |----+ 4903 | +---------+ | 4904 | | 4905 | +---------+ v 4906 | | Fine | +---+ 4907 +->| decoder |->| + | 4908 | +---------+ +---+ 4909 | ^ | 4910 +---------+ | | | 4911 | Range | | +----------+ v 4912 | Decoder |-+ | Bit | +------+ 4913 +---------+ | |Allocation| | 2**x | 4914 | +----------+ +------+ 4915 | | | 4916 | v v +--------+ 4917 | +---------+ +---+ +-------+ | pitch | 4918 +->| PVQ |->| * |->| IMDCT |->| post- |---> 4919 | | decoder | +---+ +-------+ | filter | 4920 | +---------+ +--------+ 4921 | ^ 4922 +--------------------------------------+ 4923 ]]></artwork> 4924 </figure> 4925 4926 <t> 4927 The decoder is based on the following symbols and sets of symbols: 4928 </t> 4929 4930 <texttable anchor="celt_symbols" 4931 title="Order of the Symbols in the CELT Section of the Bitstream"> 4932 <ttcol align="center">Symbol(s)</ttcol> 4933 <ttcol align="center">PDF</ttcol> 4934 <ttcol align="center">Condition</ttcol> 4935 <c>silence</c> <c>{32767, 1}/32768</c> <c></c> 4936 <c>post-filter</c> <c>{1, 1}/2</c> <c></c> 4937 <c>octave</c> <c>uniform (6)</c><c>post-filter</c> 4938 <c>period</c> <c>raw bits (4+octave)</c><c>post-filter</c> 4939 <c>gain</c> <c>raw bits (3)</c><c>post-filter</c> 4940 <c>tapset</c> <c>{2, 1, 1}/4</c><c>post-filter</c> 4941 <c>transient</c> <c>{7, 1}/8</c><c></c> 4942 <c>intra</c> <c>{7, 1}/8</c><c></c> 4943 <c>coarse energy</c><c><xref target="energy-decoding"/></c><c></c> 4944 <c>tf_change</c> <c><xref target="transient-decoding"/></c><c></c> 4945 <c>tf_select</c> <c>{1, 1}/2</c><c><xref target="transient-decoding"/></c> 4946 <c>spread</c> <c>{7, 2, 21, 2}/32</c><c></c> 4947 <c>dyn. alloc.</c> <c><xref target="allocation"/></c><c></c> 4948 <c>alloc. trim</c> <c>{2, 2, 5, 10, 22, 46, 22, 10, 5, 2, 2}/128</c><c></c> 4949 <c>skip</c> <c>{1, 1}/2</c><c><xref target="allocation"/></c> 4950 <c>intensity</c> <c>uniform</c><c><xref target="allocation"/></c> 4951 <c>dual</c> <c>{1, 1}/2</c><c></c> 4952 <c>fine energy</c> <c><xref target="energy-decoding"/></c><c></c> 4953 <c>residual</c> <c><xref target="PVQ-decoder"/></c><c></c> 4954 <c>anti-collapse</c><c>{1, 1}/2</c><c><xref target="anti-collapse"/></c> 4955 <c>finalize</c> <c><xref target="energy-decoding"/></c><c></c> 4956 </texttable> 4957 4958 <t> 4959 The decoder extracts information from the range-coded bitstream in the order 4960 described in <xref target='celt_symbols'/>. In some circumstances, it is 4961 possible for a decoded value to be out of range due to a very small amount of redundancy 4962 in the encoding of large integers by the range coder. 4963 In that case, the decoder should assume there has been an error in the coding, 4964 decoding, or transmission and SHOULD take measures to conceal the error and/or report 4965 to the application that a problem has occurred. Such out of range errors cannot occur 4966 in the SILK layer. 4967 </t> 4968 4969 <section anchor="transient-decoding" title="Transient Decoding"> 4970 <t> 4971 The "transient" flag indicates whether the frame uses a single long MDCT or several short MDCTs. 4972 When it is set, then the MDCT coefficients represent multiple 4973 short MDCTs in the frame. When not set, the coefficients represent a single 4974 long MDCT for the frame. The flag is encoded in the bitstream with a probability of 1/8. 4975 In addition to the global transient flag is a per-band 4976 binary flag to change the time-frequency (tf) resolution independently in each band. The 4977 change in tf resolution is defined in tf_select_table[][] in celt.c and depends 4978 on the frame size, whether the transient flag is set, and the value of tf_select. 4979 The tf_select flag uses a 1/2 probability, but is only decoded 4980 if it can have an impact on the result knowing the value of all per-band 4981 tf_change flags. 4982 </t> 4983 </section> 4984 4985 <section anchor="energy-decoding" title="Energy Envelope Decoding"> 4986 4987 <t> 4988 It is important to quantize the energy with sufficient resolution because 4989 any energy quantization error cannot be compensated for at a later 4990 stage. Regardless of the resolution used for encoding the spectral shape of a band, 4991 it is perceptually important to preserve the energy in each band. CELT uses a 4992 three-step coarse-fine-fine strategy for encoding the energy in the base-2 log 4993 domain, as implemented in quant_bands.c</t> 4994 4995 <section anchor="coarse-energy-decoding" title="Coarse energy decoding"> 4996 <t> 4997 Coarse quantization of the energy uses a fixed resolution of 6 dB 4998 (integer part of base-2 log). To minimize the bitrate, prediction is applied 4999 both in time (using the previous frame) and in frequency (using the previous 5000 bands). The part of the prediction that is based on the 5001 previous frame can be disabled, creating an "intra" frame where the energy 5002 is coded without reference to prior frames. The decoder first reads the intra flag 5003 to determine what prediction is used. 5004 The 2-D z-transform <xref target='z-transform'/> of 5005 the prediction filter is: 5006 <figure align="center"> 5007 <artwork align="center"><![CDATA[ 5008 -1 -1 5009 (1 - alpha*z_l )*(1 - z_b ) 5010 A(z_l, z_b) = ----------------------------- 5011 -1 5012 1 - beta*z_b 5013 ]]></artwork> 5014 </figure> 5015 where b is the band index and l is the frame index. The prediction coefficients 5016 applied depend on the frame size in use when not using intra energy and are alpha=0, beta=4915/32768 5017 when using intra energy. 5018 The time-domain prediction is based on the final fine quantization of the previous 5019 frame, while the frequency domain (within the current frame) prediction is based 5020 on coarse quantization only (because the fine quantization has not been computed 5021 yet). The prediction is clamped internally so that fixed point implementations with 5022 limited dynamic range always remain in the same state as floating point implementations. 5023 We approximate the ideal 5024 probability distribution of the prediction error using a Laplace distribution 5025 with separate parameters for each frame size in intra- and inter-frame modes. These 5026 parameters are held in the e_prob_model table in quant_bands.c. 5027 The 5028 coarse energy quantization is performed by unquant_coarse_energy() and 5029 unquant_coarse_energy_impl() (quant_bands.c). The encoding of the Laplace-distributed values is 5030 implemented in ec_laplace_decode() (laplace.c). 5031 </t> 5032 5033 </section> 5034 5035 <section anchor="fine-energy-decoding" title="Fine energy quantization"> 5036 <t> 5037 The number of bits assigned to fine energy quantization in each band is determined 5038 by the bit allocation computation described in <xref target="allocation"></xref>. 5039 Let B_i be the number of fine energy bits 5040 for band i; the refinement is an integer f in the range [0,2**B_i-1]. The mapping between f 5041 and the correction applied to the coarse energy is equal to (f+1/2)/2**B_i - 1/2. Fine 5042 energy quantization is implemented in quant_fine_energy() (quant_bands.c). 5043 </t> 5044 <t> 5045 When some bits are left "unused" after all other flags have been decoded, these bits 5046 are assigned to a "final" step of fine allocation. In effect, these bits are used 5047 to add one extra fine energy bit per band per channel. The allocation process 5048 determines two "priorities" for the final fine bits. 5049 Any remaining bits are first assigned only to bands of priority 0, starting 5050 from band 0 and going up. If all bands of priority 0 have received one bit per 5051 channel, then bands of priority 1 are assigned an extra bit per channel, 5052 starting from band 0. If any bits are left after this, they are left unused. 5053 This is implemented in unquant_energy_finalise() (quant_bands.c). 5054 </t> 5055 5056 </section> <!-- fine energy --> 5057 5058 </section> <!-- Energy decode --> 5059 5060 <section anchor="allocation" title="Bit Allocation"> 5061 5062 <t>Because the bit allocation drives the decoding of the range-coder 5063 stream, it MUST be recovered exactly so that identical coding decisions are 5064 made in the encoder and decoder. Any deviation from the reference's resulting 5065 bit allocation will result in corrupted output, though implementers are 5066 free to implement the procedure in any way which produces identical results.</t> 5067 5068 <t>The per-band gain-shape structure of the CELT layer ensures that using 5069 the same number of bits for the spectral shape of a band in every frame will 5070 result in a roughly constant signal-to-noise ratio in that band. 5071 This results in coding noise that has the same spectral envelope as the signal. 5072 The masking curve produced by a standard psychoacoustic model also closely 5073 follows the spectral envelope of the signal. 5074 This structure means that the ideal allocation is more consistent from frame to 5075 frame than it is for other codecs without an equivalent structure, and that a 5076 fixed allocation provides fairly consistent perceptual 5077 performance <xref target='Valin2010'/>.</t> 5078 5079 <t>Many codecs transmit significant amounts of side information to control the 5080 bit allocation within a frame. 5081 Often this control is only indirect, and must be exercised carefully to 5082 achieve the desired rate constraints. 5083 The CELT layer, however, can adapt over a very wide range of rates, and thus 5084 has a large number of codebook sizes to choose from for each band. 5085 Explicitly signaling the size of each of these codebooks would impose 5086 considerable overhead, even though the allocation is relatively static from 5087 frame to frame. 5088 This is because all of the information required to compute these codebook sizes 5089 must be derived from a single frame by itself, in order to retain robustness 5090 to packet loss, so the signaling cannot take advantage of knowledge of the 5091 allocation in neighboring frames. 5092 This problem is exacerbated in low-latency (small frame size) applications, 5093 which would include this overhead in every frame.</t> 5094 5095 <t>For this reason, in the MDCT mode Opus uses a primarily implicit bit 5096 allocation. The available bitstream capacity is known in advance to both 5097 the encoder and decoder without additional signaling, ultimately from the 5098 packet sizes expressed by a higher-level protocol. Using this information, 5099 the codec interpolates an allocation from a hard-coded table.</t> 5100 5101 <t>While the band-energy structure effectively models intra-band masking, 5102 it ignores the weaker inter-band masking, band-temporal masking, and 5103 other less significant perceptual effects. While these effects can 5104 often be ignored, they can become significant for particular samples. One 5105 mechanism available to encoders would be to simply increase the overall 5106 rate for these frames, but this is not possible in a constant rate mode 5107 and can be fairly inefficient. As a result three explicitly signaled 5108 mechanisms are provided to alter the implicit allocation:</t> 5109 5110 <t> 5111 <list style="symbols"> 5112 <t>Band boost</t> 5113 <t>Allocation trim</t> 5114 <t>Band skipping</t> 5115 </list> 5116 </t> 5117 5118 <t>The first of these mechanisms, band boost, allows an encoder to boost 5119 the allocation in specific bands. The second, allocation trim, works by 5120 biasing the overall allocation towards higher or lower frequency bands. The third, band 5121 skipping, selects which low-precision high frequency bands 5122 will be allocated no shape bits at all.</t> 5123 5124 <t>In stereo mode there are two additional parameters 5125 potentially coded as part of the allocation procedure: a parameter to allow the 5126 selective elimination of allocation for the 'side' (i.e., intensity stereo) in jointly coded bands, 5127 and a flag to deactivate joint coding (i.e., dual stereo). These values are not signaled if 5128 they would be meaningless in the overall context of the allocation.</t> 5129 5130 <t>Because every signaled adjustment increases overhead and implementation 5131 complexity, none were included speculatively: the reference encoder makes use 5132 of all of these mechanisms. While the decision logic in the reference was 5133 found to be effective enough to justify the overhead and complexity, further 5134 analysis techniques may be discovered which increase the effectiveness of these 5135 parameters. As with other signaled parameters, an encoder is free to choose the 5136 values in any manner, but unless a technique is known to deliver superior 5137 perceptual results the methods used by the reference implementation should be 5138 used.</t> 5139 5140 <t>The allocation process consists of the following steps: determining the per-band 5141 maximum allocation vector, decoding the boosts, decoding the tilt, determining 5142 the remaining capacity of the frame, searching the mode table for the 5143 entry nearest but not exceeding the available space (subject to the tilt, boosts, band 5144 maximums, and band minimums), linear interpolation, reallocation of 5145 unused bits with concurrent skip decoding, determination of the 5146 fine-energy vs. shape split, and final reallocation. This process results 5147 in a per-band shape allocation (in 1/8th bit units), a per-band fine-energy 5148 allocation (in 1 bit per channel units), a set of band priorities for 5149 controlling the use of remaining bits at the end of the frame, and a 5150 remaining balance of unallocated space, which is usually zero except 5151 at very high rates.</t> 5152 5153 <t> 5154 The "static" bit allocation (in 1/8 bits) for a quality q, excluding the minimums, maximums, 5155 tilt and boosts, is equal to channels*N*alloc[band][q]<<LM>>2, where 5156 alloc[][] is given in <xref target="static_alloc"/> and LM=log2(frame_size/120). The allocation 5157 is obtained by linearly interpolating between two values of q (in steps of 1/64) to find the 5158 highest allocation that does not exceed the number of bits remaining. 5159 </t> 5160 5161 <texttable anchor="static_alloc" 5162 title="CELT Static Allocation Table"> 5163 <preamble>Rows indicate the MDCT bands, columns are the different quality (q) parameters. The units are 1/32 bit per MDCT bin.</preamble> 5164 <ttcol align="right">0</ttcol> 5165 <ttcol align="right">1</ttcol> 5166 <ttcol align="right">2</ttcol> 5167 <ttcol align="right">3</ttcol> 5168 <ttcol align="right">4</ttcol> 5169 <ttcol align="right">5</ttcol> 5170 <ttcol align="right">6</ttcol> 5171 <ttcol align="right">7</ttcol> 5172 <ttcol align="right">8</ttcol> 5173 <ttcol align="right">9</ttcol> 5174 <ttcol align="right">10</ttcol> 5175 <c>0</c><c>90</c><c>110</c><c>118</c><c>126</c><c>134</c><c>144</c><c>152</c><c>162</c><c>172</c><c>200</c> 5176 <c>0</c><c>80</c><c>100</c><c>110</c><c>119</c><c>127</c><c>137</c><c>145</c><c>155</c><c>165</c><c>200</c> 5177 <c>0</c><c>75</c><c>90</c><c>103</c><c>112</c><c>120</c><c>130</c><c>138</c><c>148</c><c>158</c><c>200</c> 5178 <c>0</c><c>69</c><c>84</c><c>93</c><c>104</c><c>114</c><c>124</c><c>132</c><c>142</c><c>152</c><c>200</c> 5179 <c>0</c><c>63</c><c>78</c><c>86</c><c>95</c><c>103</c><c>113</c><c>123</c><c>133</c><c>143</c><c>200</c> 5180 <c>0</c><c>56</c><c>71</c><c>80</c><c>89</c><c>97</c><c>107</c><c>117</c><c>127</c><c>137</c><c>200</c> 5181 <c>0</c><c>49</c><c>65</c><c>75</c><c>83</c><c>91</c><c>101</c><c>111</c><c>121</c><c>131</c><c>200</c> 5182 <c>0</c><c>40</c><c>58</c><c>70</c><c>78</c><c>85</c><c>95</c><c>105</c><c>115</c><c>125</c><c>200</c> 5183 <c>0</c><c>34</c><c>51</c><c>65</c><c>72</c><c>78</c><c>88</c><c>98</c><c>108</c><c>118</c><c>198</c> 5184 <c>0</c><c>29</c><c>45</c><c>59</c><c>66</c><c>72</c><c>82</c><c>92</c><c>102</c><c>112</c><c>193</c> 5185 <c>0</c><c>20</c><c>39</c><c>53</c><c>60</c><c>66</c><c>76</c><c>86</c><c>96</c><c>106</c><c>188</c> 5186 <c>0</c><c>18</c><c>32</c><c>47</c><c>54</c><c>60</c><c>70</c><c>80</c><c>90</c><c>100</c><c>183</c> 5187 <c>0</c><c>10</c><c>26</c><c>40</c><c>47</c><c>54</c><c>64</c><c>74</c><c>84</c><c>94</c><c>178</c> 5188 <c>0</c><c>0</c><c>20</c><c>31</c><c>39</c><c>47</c><c>57</c><c>67</c><c>77</c><c>87</c><c>173</c> 5189 <c>0</c><c>0</c><c>12</c><c>23</c><c>32</c><c>41</c><c>51</c><c>61</c><c>71</c><c>81</c><c>168</c> 5190 <c>0</c><c>0</c><c>0</c><c>15</c><c>25</c><c>35</c><c>45</c><c>55</c><c>65</c><c>75</c><c>163</c> 5191 <c>0</c><c>0</c><c>0</c><c>4</c><c>17</c><c>29</c><c>39</c><c>49</c><c>59</c><c>69</c><c>158</c> 5192 <c>0</c><c>0</c><c>0</c><c>0</c><c>12</c><c>23</c><c>33</c><c>43</c><c>53</c><c>63</c><c>153</c> 5193 <c>0</c><c>0</c><c>0</c><c>0</c><c>1</c><c>16</c><c>26</c><c>36</c><c>46</c><c>56</c><c>148</c> 5194 <c>0</c><c>0</c><c>0</c><c>0</c><c>0</c><c>10</c><c>15</c><c>20</c><c>30</c><c>45</c><c>129</c> 5195 <c>0</c><c>0</c><c>0</c><c>0</c><c>0</c><c>1</c><c>1</c><c>1</c><c>1</c><c>20</c><c>104</c> 5196 </texttable> 5197 5198 <t>The maximum allocation vector is an approximation of the maximum space 5199 that can be used by each band for a given mode. The value is 5200 approximate because the shape encoding is variable rate (due 5201 to entropy coding of splitting parameters). Setting the maximum too low reduces the 5202 maximum achievable quality in a band while setting it too high 5203 may result in waste: bitstream capacity available at the end 5204 of the frame which can not be put to any use. The maximums 5205 specified by the codec reflect the average maximum. In the reference 5206 implementation, the maximums in bits/sample are precomputed in a static table 5207 (see cache_caps50[] in static_modes_float.h) for each band, 5208 for each value of LM, and for both mono and stereo. 5209 5210 Implementations are expected 5211 to simply use the same table data, but the procedure for generating 5212 this table is included in rate.c as part of compute_pulse_cache().</t> 5213 5214 <t>To convert the values in cache.caps into the actual maximums: first 5215 set nbBands to the maximum number of bands for this mode, and stereo to 5216 zero if stereo is not in use and one otherwise. For each band set N 5217 to the number of MDCT bins covered by the band (for one channel), set LM 5218 to the shift value for the frame size, 5219 then set i to nbBands*(2*LM+stereo). Then set the maximum for the band to 5220 the i-th index of cache.caps + 64 and multiply by the number of channels 5221 in the current frame (one or two) and by N, then divide the result by 4 5222 using integer division. The resulting vector will be called 5223 cap[]. The elements fit in signed 16-bit integers but do not fit in 8 bits. 5224 This procedure is implemented in the reference in the function init_caps() in celt.c. 5225 </t> 5226 5227 <t>The band boosts are represented by a series of binary symbols which 5228 are entropy coded with very low probability. Each band can potentially be boosted 5229 multiple times, subject to the frame actually having enough room to obey 5230 the boost and having enough room to code the boost symbol. The default 5231 coding cost for a boost starts out at six bits (probability p=1/64), but subsequent boosts 5232 in a band cost only a single bit and every time a band is boosted the 5233 initial cost is reduced (down to a minimum of two bits, or p=1/4). Since the initial 5234 cost of coding a boost is 6 bits, the coding cost of the boost symbols when 5235 completely unused is 0.48 bits/frame for a 21 band mode (21*-log2(1-1/2**6)).</t> 5236 5237 <t>To decode the band boosts: First set 'dynalloc_logp' to 6, the initial 5238 amount of storage required to signal a boost in bits, 'total_bits' to the 5239 size of the frame in 8th bits, 'total_boost' to zero, and 'tell' to the total number 5240 of 8th bits decoded 5241 so far. For each band from the coding start (0 normally, but 17 in Hybrid mode) 5242 to the coding end (which changes depending on the signaled bandwidth), the boost quanta 5243 in units of 1/8 bit is calculated as quanta = min(8*N, max(48, N)). 5244 This represents a boost step size of six bits, subject to a lower limit of 5245 1/8th bit/sample and an upper limit of 1 bit/sample. 5246 Set 'boost' to zero and 'dynalloc_loop_logp' 5247 to dynalloc_logp. While dynalloc_loop_log (the current worst case symbol cost) in 5248 8th bits plus tell is less than total_bits plus total_boost and boost is less than cap[] for this 5249 band: Decode a bit from the bitstream with a with dynalloc_loop_logp as the cost 5250 of a one, update tell to reflect the current used capacity, if the decoded value 5251 is zero break the loop otherwise add quanta to boost and total_boost, subtract quanta from 5252 total_bits, and set dynalloc_loop_log to 1. When the while loop finishes 5253 boost contains the boost for this band. If boost is non-zero and dynalloc_logp 5254 is greater than 2, decrease dynalloc_logp. Once this process has been 5255 executed on all bands, the band boosts have been decoded. This procedure 5256 is implemented around line 2474 of celt.c.</t> 5257 5258 <t>At very low rates it is possible that there won't be enough available 5259 space to execute the inner loop even once. In these cases band boost 5260 is not possible but its overhead is completely eliminated. Because of the 5261 high cost of band boost when activated, a reasonable encoder should not be 5262 using it at very low rates. The reference implements its dynalloc decision 5263 logic around line 1304 of celt.c.</t> 5264 5265 <t>The allocation trim is a integer value from 0-10. The default value of 5266 5 indicates no trim. The trim parameter is entropy coded in order to 5267 lower the coding cost of less extreme adjustments. Values lower than 5268 5 bias the allocation towards lower frequencies and values above 5 5269 bias it towards higher frequencies. Like other signaled parameters, signaling 5270 of the trim is gated so that it is not included if there is insufficient space 5271 available in the bitstream. To decode the trim, first set 5272 the trim value to 5, then if and only if the count of decoded 8th bits so far (ec_tell_frac) 5273 plus 48 (6 bits) is less than or equal to the total frame size in 8th 5274 bits minus total_boost (a product of the above band boost procedure), 5275 decode the trim value using the PDF in <xref target="celt_trim_pdf"/>.</t> 5276 5277 <texttable anchor="celt_trim_pdf" title="PDF for the Trim"> 5278 <ttcol>PDF</ttcol> 5279 <c>{1, 1, 2, 5, 10, 22, 46, 22, 10, 5, 2, 2}/128</c> 5280 </texttable> 5281 5282 <t>For 10 ms and 20 ms frames using short blocks and that have at least LM+2 bits left prior to 5283 the allocation process, then one anti-collapse bit is reserved in the allocation process so it can 5284 be decoded later. Following the the anti-collapse reservation, one bit is reserved for skip if available.</t> 5285 5286 <t>For stereo frames, bits are reserved for intensity stereo and for dual stereo. Intensity stereo 5287 requires ilog2(end-start) bits. Those bits are reserved if there is enough bits left. Following this, one 5288 bit is reserved for dual stereo if available.</t> 5289 5290 5291 <t>The allocation computation begins by setting up some initial conditions. 5292 'total' is set to the remaining available 8th bits, computed by taking the 5293 size of the coded frame times 8 and subtracting ec_tell_frac(). From this value, one (8th bit) 5294 is subtracted to ensure that the resulting allocation will be conservative. 'anti_collapse_rsv' 5295 is set to 8 (8th bits) if and only if the frame is a transient, LM is greater than 1, and total is 5296 greater than or equal to (LM+2) * 8. Total is then decremented by anti_collapse_rsv and clamped 5297 to be equal to or greater than zero. 'skip_rsv' is set to 8 (8th bits) if total is greater than 5298 8, otherwise it is zero. Total is then decremented by skip_rsv. This reserves space for the 5299 final skipping flag.</t> 5300 5301 <t>If the current frame is stereo, intensity_rsv is set to the conservative log2 in 8th bits 5302 of the number of coded bands for this frame (given by the table LOG2_FRAC_TABLE in rate.c). If 5303 intensity_rsv is greater than total then intensity_rsv is set to zero. Otherwise total is 5304 decremented by intensity_rsv, and if total is still greater than 8, dual_stereo_rsv is 5305 set to 8 and total is decremented by dual_stereo_rsv.</t> 5306 5307 <t>The allocation process then computes a vector representing the hard minimum amounts allocation 5308 any band will receive for shape. This minimum is higher than the technical limit of the PVQ 5309 process, but very low rate allocations produce an excessively sparse spectrum and these bands 5310 are better served by having no allocation at all. For each coded band, set thresh[band] to 5311 twenty-four times the number of MDCT bins in the band and divide by 16. If 8 times the number 5312 of channels is greater, use that instead. This sets the minimum allocation to one bit per channel 5313 or 48 128th bits per MDCT bin, whichever is greater. The band-size dependent part of this 5314 value is not scaled by the channel count, because at the very low rates where this limit is 5315 applicable there will usually be no bits allocated to the side.</t> 5316 5317 <t>The previously decoded allocation trim is used to derive a vector of per-band adjustments, 5318 'trim_offsets[]'. For each coded band take the alloc_trim and subtract 5 and LM. Then multiply 5319 the result by the number of channels, the number of MDCT bins in the shortest frame size for this mode, 5320 the number of remaining bands, 2**LM, and 8. Then divide this value by 64. Finally, if the 5321 number of MDCT bins in the band per channel is only one, 8 times the number of channels is subtracted 5322 in order to diminish the allocation by one bit, because width 1 bands receive greater benefit 5323 from the coarse energy coding.</t> 5324 5325 5326 </section> 5327 5328 <section anchor="PVQ-decoder" title="Shape Decoding"> 5329 <t> 5330 In each band, the normalized "shape" is encoded 5331 using a vector quantization scheme called a "pyramid vector quantizer". 5332 </t> 5333 5334 <t>In 5335 the simplest case, the number of bits allocated in 5336 <xref target="allocation"></xref> is converted to a number of pulses as described 5337 by <xref target="bits-pulses"></xref>. Knowing the number of pulses and the 5338 number of samples in the band, the decoder calculates the size of the codebook 5339 as detailed in <xref target="cwrs-decoder"></xref>. The size is used to decode 5340 an unsigned integer (uniform probability model), which is the codeword index. 5341 This index is converted into the corresponding vector as explained in 5342 <xref target="cwrs-decoder"></xref>. This vector is then scaled to unit norm. 5343 </t> 5344 5345 <section anchor="bits-pulses" title="Bits to Pulses"> 5346 <t> 5347 Although the allocation is performed in 1/8th bit units, the quantization requires 5348 an integer number of pulses K. To do this, the encoder searches for the value 5349 of K that produces the number of bits nearest to the allocated value 5350 (rounding down if exactly halfway between two values), not to exceed 5351 the total number of bits available. For efficiency reasons, the search is performed against a 5352 precomputed allocation table which only permits some K values for each N. The number of 5353 codebook entries can be computed as explained in <xref target="cwrs-decoder"></xref>. The difference 5354 between the number of bits allocated and the number of bits used is accumulated to a 5355 "balance" (initialized to zero) that helps adjust the 5356 allocation for the next bands. One third of the balance is applied to the 5357 bit allocation of each band to help achieve the target allocation. The only 5358 exceptions are the band before the last and the last band, for which half the balance 5359 and the whole balance are applied, respectively. 5360 </t> 5361 </section> 5362 5363 <section anchor="cwrs-decoder" title="PVQ Decoding"> 5364 5365 <t> 5366 Decoding of PVQ vectors is implemented in decode_pulses() (cwrs.c). 5367 The unique codeword index is decoded as a uniformly-distributed integer value between 0 and 5368 V(N,K)-1, where V(N,K) is the number of possible combinations of K pulses in 5369 N samples. The index is then converted to a vector in the same way specified in 5370 <xref target="PVQ"></xref>. The indexing is based on the calculation of V(N,K) 5371 (denoted N(L,K) in <xref target="PVQ"></xref>). 5372 </t> 5373 5374 <t> 5375 The number of combinations can be computed recursively as 5376 V(N,K) = V(N-1,K) + V(N,K-1) + V(N-1,K-1), with V(N,0) = 1 and V(0,K) = 0, K != 0. 5377 There are many different ways to compute V(N,K), including precomputed tables and direct 5378 use of the recursive formulation. The reference implementation applies the recursive 5379 formulation one line (or column) at a time to save on memory use, 5380 along with an alternate, 5381 univariate recurrence to initialize an arbitrary line, and direct 5382 polynomial solutions for small N. All of these methods are 5383 equivalent, and have different trade-offs in speed, memory usage, and 5384 code size. Implementations MAY use any methods they like, as long as 5385 they are equivalent to the mathematical definition. 5386 </t> 5387 5388 <t> 5389 The decoded vector X is recovered as follows. 5390 Let i be the index decoded with the procedure in <xref target="ec_dec_uint"/> 5391 with ft = V(N,K), so that 0 <= i < V(N,K). 5392 Let k = K. 5393 Then for j = 0 to (N - 1), inclusive, do: 5394 <list style="numbers"> 5395 <t>Let p = (V(N-j-1,k) + V(N-j,k))/2.</t> 5396 <t> 5397 If i < p, then let sgn = 1, else let sgn = -1 5398 and set i = i - p. 5399 </t> 5400 <t>Let k0 = k and set p = p - V(N-j-1,k).</t> 5401 <t> 5402 While p > i, set k = k - 1 and 5403 p = p - V(N-j-1,k). 5404 </t> 5405 <t> 5406 Set X[j] = sgn*(k0 - k) and i = i - p. 5407 </t> 5408 </list> 5409 </t> 5410 5411 <t> 5412 The decoded vector X is then normalized such that its 5413 L2-norm equals one. 5414 </t> 5415 </section> 5416 5417 <section anchor="spreading" title="Spreading"> 5418 <t> 5419 The normalized vector decoded in <xref target="cwrs-decoder"/> is then rotated 5420 for the purpose of avoiding tonal artifacts. The rotation gain is equal to 5421 <figure align="center"> 5422 <artwork align="center"><![CDATA[ 5423 g_r = N / (N + f_r*K) 5424 ]]></artwork> 5425 </figure> 5426 5427 where N is the number of dimensions, K is the number of pulses, and f_r depends on 5428 the value of the "spread" parameter in the bit-stream. 5429 </t> 5430 5431 <texttable anchor="spread values" title="Spreading Values"> 5432 <ttcol>Spread value</ttcol> 5433 <ttcol>f_r</ttcol> 5434 <c>0</c> <c>infinite (no rotation)</c> 5435 <c>1</c> <c>15</c> 5436 <c>2</c> <c>10</c> 5437 <c>3</c> <c>5</c> 5438 </texttable> 5439 5440 <t> 5441 The rotation angle is then calculated as 5442 <figure align="center"> 5443 <artwork align="center"><![CDATA[ 5444 2 5445 pi * g_r 5446 theta = ---------- 5447 4 5448 ]]></artwork> 5449 </figure> 5450 A 2-D rotation R(i,j) between points x_i and x_j is defined as: 5451 <figure align="center"> 5452 <artwork align="center"><![CDATA[ 5453 x_i' = cos(theta)*x_i + sin(theta)*x_j 5454 x_j' = -sin(theta)*x_i + cos(theta)*x_j 5455 ]]></artwork> 5456 </figure> 5457 5458 An N-D rotation is then achieved by applying a series of 2-D rotations back and forth, in the 5459 following order: R(x_1, x_2), R(x_2, x_3), ..., R(x_N-2, X_N-1), R(x_N-1, X_N), 5460 R(x_N-2, X_N-1), ..., R(x_1, x_2). 5461 </t> 5462 5463 <t> 5464 If the decoded vector represents more 5465 than one time block, then this spreading process is applied separately on each time block. 5466 Also, if each block represents 8 samples or more, then another N-D rotation, by 5467 (pi/2-theta), is applied <spanx style="emph">before</spanx> the rotation described above. This 5468 extra rotation is applied in an interleaved manner with a stride equal to round(sqrt(N/nb_blocks)), 5469 i.e., it is applied independently for each set of sample S_k = {stride*n + k}, n=0..N/stride-1. 5470 </t> 5471 </section> 5472 5473 <section anchor="split" title="Split decoding"> 5474 <t> 5475 To avoid the need for multi-precision calculations when decoding PVQ codevectors, 5476 the maximum size allowed for codebooks is 32 bits. When larger codebooks are 5477 needed, the vector is instead split in two sub-vectors of size N/2. 5478 A quantized gain parameter with precision 5479 derived from the current allocation is entropy coded to represent the relative 5480 gains of each side of the split, and the entire decoding process is recursively 5481 applied. Multiple levels of splitting may be applied up to a limit of LM+1 splits. 5482 The same recursive mechanism is applied for the joint coding 5483 of stereo audio. 5484 </t> 5485 5486 </section> 5487 5488 <section anchor="tf-change" title="Time-Frequency change"> 5489 <t> 5490 The time-frequency (TF) parameters are used to control the time-frequency resolution tradeoff 5491 in each coded band. For each band, there are two possible TF choices. For the first 5492 band coded, the PDF is {3, 1}/4 for frames marked as transient and {15, 1}/16 for 5493 the other frames. For subsequent bands, the TF choice is coded relative to the 5494 previous TF choice with probability {15, 1}/15 for transient frames and {31, 1}/32 5495 otherwise. The mapping between the decoded TF choices and the adjustment in TF 5496 resolution is shown in the tables below. 5497 </t> 5498 5499 <texttable anchor='tf_00' 5500 title="TF Adjustments for Non-transient Frames and tf_select=0"> 5501 <ttcol align='center'>Frame size (ms)</ttcol> 5502 <ttcol align='center'>0</ttcol> 5503 <ttcol align='center'>1</ttcol> 5504 <c>2.5</c> <c>0</c> <c>-1</c> 5505 <c>5</c> <c>0</c> <c>-1</c> 5506 <c>10</c> <c>0</c> <c>-2</c> 5507 <c>20</c> <c>0</c> <c>-2</c> 5508 </texttable> 5509 5510 <texttable anchor='tf_01' 5511 title="TF Adjustments for Non-transient Frames and tf_select=1"> 5512 <ttcol align='center'>Frame size (ms)</ttcol> 5513 <ttcol align='center'>0</ttcol> 5514 <ttcol align='center'>1</ttcol> 5515 <c>2.5</c> <c>0</c> <c>-1</c> 5516 <c>5</c> <c>0</c> <c>-2</c> 5517 <c>10</c> <c>0</c> <c>-3</c> 5518 <c>20</c> <c>0</c> <c>-3</c> 5519 </texttable> 5520 5521 5522 <texttable anchor='tf_10' 5523 title="TF Adjustments for Transient Frames and tf_select=0"> 5524 <ttcol align='center'>Frame size (ms)</ttcol> 5525 <ttcol align='center'>0</ttcol> 5526 <ttcol align='center'>1</ttcol> 5527 <c>2.5</c> <c>0</c> <c>-1</c> 5528 <c>5</c> <c>1</c> <c>0</c> 5529 <c>10</c> <c>2</c> <c>0</c> 5530 <c>20</c> <c>3</c> <c>0</c> 5531 </texttable> 5532 5533 <texttable anchor='tf_11' 5534 title="TF Adjustments for Transient Frames and tf_select=1"> 5535 <ttcol align='center'>Frame size (ms)</ttcol> 5536 <ttcol align='center'>0</ttcol> 5537 <ttcol align='center'>1</ttcol> 5538 <c>2.5</c> <c>0</c> <c>-1</c> 5539 <c>5</c> <c>1</c> <c>-1</c> 5540 <c>10</c> <c>1</c> <c>-1</c> 5541 <c>20</c> <c>1</c> <c>-1</c> 5542 </texttable> 5543 5544 <t> 5545 A negative TF adjustment means that the temporal resolution is increased, 5546 while a positive TF adjustment means that the frequency resolution is increased. 5547 Changes in TF resolution are implemented using the Hadamard transform <xref target="Hadamard"/>. To increase 5548 the time resolution by N, N "levels" of the Hadamard transform are applied to the 5549 decoded vector for each interleaved MDCT vector. To increase the frequency resolution 5550 (assumes a transient frame), then N levels of the Hadamard transform are applied 5551 <spanx style="emph">across</spanx> the interleaved MDCT vector. In the case of increased 5552 time resolution the decoder uses the "sequency order" because the input vector 5553 is sorted in time. 5554 </t> 5555 </section> 5556 5557 5558 </section> 5559 5560 <section anchor="anti-collapse" title="Anti-Collapse Processing"> 5561 <t> 5562 The anti-collapse feature is designed to avoid the situation where the use of multiple 5563 short MDCTs causes the energy in one or more of the MDCTs to be zero for 5564 some bands, causing unpleasant artifacts. 5565 When the frame has the transient bit set, an anti-collapse bit is decoded. 5566 When anti-collapse is set, the energy in each small MDCT is prevented 5567 from collapsing to zero. For each band of each MDCT where a collapse is 5568 detected, a pseudo-random signal is inserted with an energy corresponding 5569 to the minimum energy over the two previous frames. A renormalization step is 5570 then required to ensure that the anti-collapse step did not alter the 5571 energy preservation property. 5572 </t> 5573 </section> 5574 5575 <section anchor="denormalization" title="Denormalization"> 5576 <t> 5577 Just as each band was normalized in the encoder, the last step of the decoder before 5578 the inverse MDCT is to denormalize the bands. Each decoded normalized band is 5579 multiplied by the square root of the decoded energy. This is done by denormalise_bands() 5580 (bands.c). 5581 </t> 5582 </section> 5583 5584 <section anchor="inverse-mdct" title="Inverse MDCT"> 5585 5586 5587 <t>The inverse MDCT implementation has no special characteristics. The 5588 input is N frequency-domain samples and the output is 2*N time-domain 5589 samples, while scaling by 1/2. A "low-overlap" window reduces the algorithmic delay. 5590 It is derived from a basic (full overlap) 240-sample version of the window used by the Vorbis codec: 5591 <figure align="center"> 5592 <artwork align="center"><![CDATA[ 5593 2 5594 / /pi /pi n + 1/2\ \ \ 5595 W(n) = |sin|-- * sin|-- * -------| | | . 5596 \ \2 \2 L / / / 5597 ]]></artwork> 5598 </figure> 5599 The low-overlap window is created by zero-padding the basic window and inserting ones in the 5600 middle, such that the resulting window still satisfies power complementarity <xref target='Princen86'/>. 5601 The IMDCT and 5602 windowing are performed by mdct_backward (mdct.c). 5603 </t> 5604 5605 <section anchor="post-filter" title="Post-filter"> 5606 <t> 5607 The output of the inverse MDCT (after weighted overlap-add) is sent to the 5608 post-filter. Although the post-filter is applied at the end, the post-filter 5609 parameters are encoded at the beginning, just after the silence flag. 5610 The post-filter can be switched on or off using one bit (logp=1). 5611 If the post-filter is enabled, then the octave is decoded as an integer value 5612 between 0 and 6 of uniform probability. Once the octave is known, the fine pitch 5613 within the octave is decoded using 4+octave raw bits. The final pitch period 5614 is equal to (16<<octave)+fine_pitch-1 so it is bounded between 15 and 1022, 5615 inclusively. Next, the gain is decoded as three raw bits and is equal to 5616 G=3*(int_gain+1)/32. The set of post-filter taps is decoded last, using 5617 a pdf equal to {2, 1, 1}/4. Tapset zero corresponds to the filter coefficients 5618 g0 = 0.3066406250, g1 = 0.2170410156, g2 = 0.1296386719. Tapset one 5619 corresponds to the filter coefficients g0 = 0.4638671875, g1 = 0.2680664062, 5620 g2 = 0, and tapset two uses filter coefficients g0 = 0.7998046875, 5621 g1 = 0.1000976562, g2 = 0. 5622 </t> 5623 5624 <t> 5625 The post-filter response is thus computed as: 5626 <figure align="center"> 5627 <artwork align="center"> 5628 <![CDATA[ 5629 y(n) = x(n) + G*(g0*y(n-T) + g1*(y(n-T+1)+y(n-T+1)) 5630 + g2*(y(n-T+2)+y(n-T+2))) 5631 ]]> 5632 </artwork> 5633 </figure> 5634 5635 During a transition between different gains, a smooth transition is calculated 5636 using the square of the MDCT window. It is important that values of y(n) be 5637 interpolated one at a time such that the past value of y(n) used is interpolated. 5638 </t> 5639 </section> 5640 5641 <section anchor="deemphasis" title="De-emphasis"> 5642 <t> 5643 After the post-filter, 5644 the signal is de-emphasized using the inverse of the pre-emphasis filter 5645 used in the encoder: 5646 <figure align="center"> 5647 <artwork align="center"><![CDATA[ 5648 1 1 5649 ---- = --------------- , 5650 A(z) -1 5651 1 - alpha_p*z 5652 ]]></artwork> 5653 </figure> 5654 where alpha_p=0.8500061035. 5655 </t> 5656 </section> 5657 5658 </section> 5659 5660 </section> 5661 5662 <section anchor="Packet Loss Concealment" title="Packet Loss Concealment (PLC)"> 5663 <t> 5664 Packet loss concealment (PLC) is an optional decoder-side feature that 5665 SHOULD be included when receiving from an unreliable channel. Because 5666 PLC is not part of the bitstream, there are many acceptable ways to 5667 implement PLC with different complexity/quality trade-offs. 5668 </t> 5669 5670 <t> 5671 The PLC in 5672 the reference implementation depends on the mode of last packet received. 5673 In CELT mode, the PLC finds a periodicity in the decoded 5674 signal and repeats the windowed waveform using the pitch offset. The windowed 5675 waveform is overlapped in such a way as to preserve the time-domain aliasing 5676 cancellation with the previous frame and the next frame. This is implemented 5677 in celt_decode_lost() (mdct.c). In SILK mode, the PLC uses LPC extrapolation 5678 from the previous frame, implemented in silk_PLC() (PLC.c). 5679 </t> 5680 5681 <section anchor="clock-drift" title="Clock Drift Compensation"> 5682 <t> 5683 Clock drift refers to the gradual desynchronization of two endpoints 5684 whose sample clocks run at different frequencies while they are streaming 5685 live audio. Differences in clock frequencies are generally attributable to 5686 manufacturing variation in the endpoints' clock hardware. For long-lived 5687 streams, the time difference between sender and receiver can grow without 5688 bound. 5689 </t> 5690 5691 <t> 5692 When the sender's clock runs slower than the receiver's, the effect is similar 5693 to packet loss: too few packets are received. The receiver can distinguish 5694 between drift and loss if the transport provides packet timestamps. A receiver 5695 for live streams SHOULD conceal the effects of drift, and MAY do so by invoking 5696 the PLC. 5697 </t> 5698 5699 <t> 5700 When the sender's clock runs faster than the receiver's, too many packets will 5701 be received. The receiver MAY respond by skipping any packet (i.e., not 5702 submitting the packet for decoding). This is likely to produce a less severe 5703 artifact than if the frame were dropped after decoding. 5704 </t> 5705 5706 <t> 5707 A decoder MAY employ a more sophisticated drift compensation method. For 5708 example, the 5709 <xref target='Google-NetEQ'>NetEQ component</xref> 5710 of the 5711 <xref target='Google-WebRTC'>Google WebRTC codebase</xref> 5712 compensates for drift by adding or removing 5713 one period when the signal is highly periodic. The reference implementation of 5714 Opus allows a caller to learn whether the current frame's signal is highly 5715 periodic, and if so what the period is, using the OPUS_GET_PITCH() request. 5716 </t> 5717 </section> 5718 5719 </section> 5720 5721 <section anchor="switching" title="Configuration Switching"> 5722 5723 <t> 5724 Switching between the Opus coding modes, audio bandwidths, and channel counts 5725 requires careful consideration to avoid audible glitches. 5726 Switching between any two configurations of the CELT-only mode, any two 5727 configurations of the Hybrid mode, or from WB SILK to Hybrid mode does not 5728 require any special treatment in the decoder, as the MDCT overlap will smooth 5729 the transition. 5730 Switching from Hybrid mode to WB SILK requires adding in the final contents 5731 of the CELT overlap buffer to the first SILK-only packet. 5732 This can be done by decoding a 2.5 ms silence frame with the CELT decoder 5733 using the channel count of the SILK-only packet (and any choice of audio 5734 bandwidth), which will correctly handle the cases when the channel count 5735 changes as well. 5736 </t> 5737 5738 <t> 5739 When changing the channel count for SILK-only or Hybrid packets, the encoder 5740 can avoid glitches by smoothly varying the stereo width of the input signal 5741 before or after the transition, and SHOULD do so. 5742 However, other transitions between SILK-only packets or between NB or MB SILK 5743 and Hybrid packets may cause glitches, because neither the LSF coefficients 5744 nor the LTP, LPC, stereo unmixing, and resampler buffers are available at the 5745 new sample rate. 5746 These switches SHOULD be delayed by the encoder until quiet periods or 5747 transients, where the inevitable glitches will be less audible. Additionally, 5748 the bit-stream MAY include redundant side information ("redundancy"), in the 5749 form of additional CELT frames embedded in each of the Opus frames around the 5750 transition. 5751 </t> 5752 5753 <t> 5754 The other transitions that cannot be easily handled are those where the lower 5755 frequencies switch between the SILK LP-based model and the CELT MDCT model. 5756 However, an encoder may not have an opportunity to delay such a switch to a 5757 convenient point. 5758 For example, if the content switches from speech to music, and the encoder does 5759 not have enough latency in its analysis to detect this in advance, there may 5760 be no convenient silence period during which to make the transition for quite 5761 some time. 5762 To avoid or reduce glitches during these problematic mode transitions, and 5763 also between audio bandwidth changes in the SILK-only modes, transitions MAY 5764 include redundant side information ("redundancy"), in the form of an 5765 additional CELT frame embedded in the Opus frame. 5766 </t> 5767 5768 <t> 5769 A transition between coding the lower frequencies with the LP model and the 5770 MDCT model or a transition that involves changing the SILK bandwidth 5771 is only normatively specified when it includes redundancy. 5772 For those without redundancy, it is RECOMMENDED that the decoder use a 5773 concealment technique (e.g., make use of a PLC algorithm) to "fill in" the 5774 gap or discontinuity caused by the mode transition. 5775 Therefore, PLC MUST NOT be applied during any normative transition, i.e., when 5776 <list style="symbols"> 5777 <t>A packet includes redundancy for this transition (as described below),</t> 5778 <t>The transition is between any WB SILK packet and any Hybrid packet, or vice 5779 versa,</t> 5780 <t>The transition is between any two Hybrid mode packets, or</t> 5781 <t>The transition is between any two CELT mode packets,</t> 5782 </list> 5783 unless there is actual packet loss. 5784 </t> 5785 5786 <section anchor="side-info" title="Transition Side Information (Redundancy)"> 5787 <t> 5788 Transitions with side information include an extra 5 ms "redundant" CELT 5789 frame within the Opus frame. 5790 This frame is designed to fill in the gap or discontinuity in the different 5791 layers without requiring the decoder to conceal it. 5792 For transitions from CELT-only to SILK-only or Hybrid, the redundant frame is 5793 inserted in the first Opus frame after the transition (i.e., the first 5794 SILK-only or Hybrid frame). 5795 For transitions from SILK-only or Hybrid to CELT-only, the redundant frame is 5796 inserted in the last Opus frame before the transition (i.e., the last 5797 SILK-only or Hybrid frame). 5798 </t> 5799 5800 <section anchor="opus_redundancy_flag" title="Redundancy Flag"> 5801 <t> 5802 The presence of redundancy is signaled in all SILK-only and Hybrid frames, not 5803 just those involved in a mode transition. 5804 This allows the frames to be decoded correctly even if an adjacent frame is 5805 lost. 5806 For SILK-only frames, this signaling is implicit, based on the size of the 5807 of the Opus frame and the number of bits consumed decoding the SILK portion of 5808 it. 5809 After decoding the SILK portion of the Opus frame, the decoder uses ec_tell() 5810 (see <xref target="ec_tell"/>) to check if there are at least 17 bits 5811 remaining. 5812 If so, then the frame contains redundancy. 5813 </t> 5814 5815 <t> 5816 For Hybrid frames, this signaling is explicit. 5817 After decoding the SILK portion of the Opus frame, the decoder uses ec_tell() 5818 (see <xref target="ec_tell"/>) to ensure there are at least 37 bits remaining. 5819 If so, it reads a symbol with the PDF in 5820 <xref target="opus_redundancy_flag_pdf"/>, and if the value is 1, then the 5821 frame contains redundancy. 5822 Otherwise (if there were fewer than 37 bits left or the value was 0), the frame 5823 does not contain redundancy. 5824 </t> 5825 5826 <texttable anchor="opus_redundancy_flag_pdf" title="Redundancy Flag PDF"> 5827 <ttcol>PDF</ttcol> 5828 <c>{4095, 1}/4096</c> 5829 </texttable> 5830 </section> 5831 5832 <section anchor="opus_redundancy_pos" title="Redundancy Position Flag"> 5833 <t> 5834 Since the current frame is a SILK-only or a Hybrid frame, it must be at least 5835 10 ms. 5836 Therefore, it needs an additional flag to indicate whether the redundant 5837 5 ms CELT frame should be mixed into the beginning of the current frame, 5838 or the end. 5839 After determining that a frame contains redundancy, the decoder reads a 5840 1 bit symbol with a uniform PDF 5841 (<xref target="opus_redundancy_pos_pdf"/>). 5842 </t> 5843 5844 <texttable anchor="opus_redundancy_pos_pdf" title="Redundancy Position PDF"> 5845 <ttcol>PDF</ttcol> 5846 <c>{1, 1}/2</c> 5847 </texttable> 5848 5849 <t> 5850 If the value is zero, this is the first frame in the transition, and the 5851 redundancy belongs at the end. 5852 If the value is one, this is the second frame in the transition, and the 5853 redundancy belongs at the beginning. 5854 There is no way to specify that an Opus frame contains separate redundant CELT 5855 frames at both the beginning and the end. 5856 </t> 5857 </section> 5858 5859 <section anchor="opus_redundancy_size" title="Redundancy Size"> 5860 <t> 5861 Unlike the CELT portion of a Hybrid frame, the redundant CELT frame does not 5862 use the same entropy coder state as the rest of the Opus frame, because this 5863 would break the CELT bit allocation mechanism in Hybrid frames. 5864 Thus, a redundant CELT frame always starts and ends on a byte boundary, even in 5865 SILK-only frames, where this is not strictly necessary. 5866 </t> 5867 5868 <t> 5869 For SILK-only frames, the number of bytes in the redundant CELT frame is simply 5870 the number of whole bytes remaining, which must be at least 2, due to the 5871 space check in <xref target="opus_redundancy_flag"/>. 5872 For Hybrid frames, the number of bytes is equal to 2, plus a decoded unsigned 5873 integer less than 256 (see <xref target="ec_dec_uint"/>). 5874 This may be more than the number of whole bytes remaining in the Opus frame, 5875 in which case the frame is invalid. 5876 However, a decoder is not required to ignore the entire frame, as this may be 5877 the result of a bit error that desynchronized the range coder. 5878 There may still be useful data before the error, and a decoder MAY keep any 5879 audio decoded so far instead of invoking the PLC, but it is RECOMMENDED that 5880 the decoder stop decoding and discard the rest of the current Opus frame. 5881 </t> 5882 5883 <t> 5884 It would have been possible to avoid these invalid states in the design of Opus 5885 by limiting the range of the explicit length decoded from Hybrid frames by the 5886 actual number of whole bytes remaining. 5887 However, this would require an encoder to determine the rate allocation for the 5888 MDCT layer up front, before it began encoding that layer. 5889 By allowing some invalid sizes, the encoder is able to defer that decision 5890 until much later. 5891 When encoding Hybrid frames which do not include redundancy, the encoder must 5892 still decide up-front if it wishes to use the minimum 37 bits required to 5893 trigger encoding of the redundancy flag, but this is a much looser 5894 restriction. 5895 </t> 5896 5897 <t> 5898 After determining the size of the redundant CELT frame, the decoder reduces 5899 the size of the buffer currently in use by the range coder by that amount. 5900 The CELT layer read any raw bits from the end of this reduced buffer, and all 5901 calculations of the number of bits remaining in the buffer must be done using 5902 this new, reduced size, rather than the original size of the Opus frame. 5903 </t> 5904 </section> 5905 5906 <section anchor="opus_redundancy_decoding" title="Decoding the Redundancy"> 5907 <t> 5908 The redundant frame is decoded like any other CELT-only frame, with the 5909 exception that it does not contain a TOC byte. 5910 The frame size is fixed at 5 ms, the channel count is set to that of the 5911 current frame, and the audio bandwidth is also set to that of the current 5912 frame, with the exception that for MB SILK frames, it is set to WB. 5913 </t> 5914 5915 <t> 5916 If the redundancy belongs at the beginning (in a CELT-only to SILK-only or 5917 Hybrid transition), the final reconstructed output uses the first 2.5 ms 5918 of audio output by the decoder for the redundant frame as-is, discarding 5919 the corresponding output from the SILK-only or Hybrid portion of the frame. 5920 The remaining 2.5 ms is cross-lapped with the decoded SILK/Hybrid signal 5921 using the CELT's power-complementary MDCT window to ensure a smooth 5922 transition. 5923 </t> 5924 5925 <t> 5926 If the redundancy belongs at the end (in a SILK-only or Hybrid to CELT-only 5927 transition), only the second half (2.5 ms) of the audio output by the 5928 decoder for the redundant frame is used. 5929 In that case, the second half of the redundant frame is cross-lapped with the 5930 end of the SILK/Hybrid signal, again using CELT's power-complementary MDCT 5931 window to ensure a smooth transition. 5932 </t> 5933 </section> 5934 5935 </section> 5936 5937 <section anchor="decoder-reset" title="State Reset"> 5938 <t> 5939 When a transition occurs, the state of the SILK or the CELT decoder (or both) 5940 may need to be reset before decoding a frame in the new mode. 5941 This avoids reusing "out of date" memory, which may not have been updated in 5942 some time or may not be in a well-defined state due to, e.g., PLC. 5943 The SILK state is reset before every SILK-only or Hybrid frame where the 5944 previous frame was CELT-only. 5945 The CELT state is reset every time the operating mode changes and the new mode 5946 is either Hybrid or CELT-only, except when the transition uses redundancy as 5947 described above. 5948 When switching from SILK-only or Hybrid to CELT-only with redundancy, the CELT 5949 state is reset before decoding the redundant CELT frame embedded in the 5950 SILK-only or Hybrid frame, but it is not reset before decoding the following 5951 CELT-only frame. 5952 When switching from CELT-only mode to SILK-only or Hybrid mode with redundancy, 5953 the CELT decoder is not reset for decoding the redundant CELT frame. 5954 </t> 5955 </section> 5956 5957 <section title="Summary of Transitions"> 5958 5959 <t> 5960 <xref target="normative_transitions"/> illustrates all of the normative 5961 transitions involving a mode change, an audio bandwidth change, or both. 5962 Each one uses an S, H, or C to represent an Opus frame in the corresponding 5963 mode. 5964 In addition, an R indicates the presence of redundancy in the Opus frame it is 5965 cross-lapped with. 5966 Its location in the first or last 5 ms is assumed to correspond to whether 5967 it is the frame before or after the transition. 5968 Other uses of redundancy are non-normative. 5969 Finally, a c indicates the contents of the CELT overlap buffer after the 5970 previously decoded frame (i.e., as extracted by decoding a silence frame). 5971 <figure align="center" anchor="normative_transitions" 5972 title="Normative Transitions"> 5973 <artwork align="center"><![CDATA[ 5974 SILK to SILK with Redundancy: S -> S -> S 5975 & 5976 !R -> R 5977 & 5978 ;S -> S -> S 5979 5980 NB or MB SILK to Hybrid with Redundancy: S -> S -> S 5981 & 5982 !R ->;H -> H -> H 5983 5984 WB SILK to Hybrid: S -> S -> S ->!H -> H -> H 5985 5986 SILK to CELT with Redundancy: S -> S -> S 5987 & 5988 !R -> C -> C -> C 5989 5990 Hybrid to NB or MB SILK with Redundancy: H -> H -> H 5991 & 5992 !R -> R 5993 & 5994 ;S -> S -> S 5995 5996 Hybrid to WB SILK: H -> H -> H -> c 5997 \ + 5998 > S -> S -> S 5999 6000 Hybrid to CELT with Redundancy: H -> H -> H 6001 & 6002 !R -> C -> C -> C 6003 6004 CELT to SILK with Redundancy: C -> C -> C -> R 6005 & 6006 ;S -> S -> S 6007 6008 CELT to Hybrid with Redundancy: C -> C -> C -> R 6009 & 6010 |H -> H -> H 6011 6012 Key: 6013 S SILK-only frame ; SILK decoder reset 6014 H Hybrid frame | CELT and SILK decoder resets 6015 C CELT-only frame ! CELT decoder reset 6016 c CELT overlap + Direct mixing 6017 R Redundant CELT frame & Windowed cross-lap 6018 ]]></artwork> 6019 </figure> 6020 The first two and the last two Opus frames in each example are illustrative, 6021 i.e., there is no requirement that a stream remain in the same configuration 6022 for three consecutive frames before or after a switch. 6023 </t> 6024 6025 <t> 6026 The behavior of transitions without redundancy where PLC is allowed is non-normative. 6027 An encoder might still wish to use these transitions if, for example, it 6028 doesn't want to add the extra bitrate required for redundancy or if it makes 6029 a decision to switch after it has already transmitted the frame that would 6030 have had to contain the redundancy. 6031 <xref target="nonnormative_transitions"/> illustrates the recommended 6032 cross-lapping and decoder resets for these transitions. 6033 <figure align="center" anchor="nonnormative_transitions" 6034 title="Recommended Non-Normative Transitions"> 6035 <artwork align="center"><![CDATA[ 6036 SILK to SILK (audio bandwidth change): S -> S -> S ;S -> S -> S 6037 6038 NB or MB SILK to Hybrid: S -> S -> S |H -> H -> H 6039 6040 SILK to CELT without Redundancy: S -> S -> S -> P 6041 & 6042 !C -> C -> C 6043 6044 Hybrid to NB or MB SILK: H -> H -> H -> c 6045 + 6046 ;S -> S -> S 6047 6048 Hybrid to CELT without Redundancy: H -> H -> H -> P 6049 & 6050 !C -> C -> C 6051 6052 CELT to SILK without Redundancy: C -> C -> C -> P 6053 & 6054 ;S -> S -> S 6055 6056 CELT to Hybrid without Redundancy: C -> C -> C -> P 6057 & 6058 |H -> H -> H 6059 6060 Key: 6061 S SILK-only frame ; SILK decoder reset 6062 H Hybrid frame | CELT and SILK decoder resets 6063 C CELT-only frame ! CELT decoder reset 6064 c CELT overlap + Direct mixing 6065 P Packet Loss Concealment & Windowed cross-lap 6066 ]]></artwork> 6067 </figure> 6068 Encoders SHOULD NOT use other transitions, e.g., those that involve redundancy 6069 in ways not illustrated in <xref target="normative_transitions"/>. 6070 </t> 6071 6072 </section> 6073 6074 </section> 6075 6076 </section> 6077 6078 6079 <!-- ******************************************************************* --> 6080 <!-- ************************** OPUS ENCODER *********************** --> 6081 <!-- ******************************************************************* --> 6082 6083 <section title="Opus Encoder"> 6084 <t> 6085 Just like the decoder, the Opus encoder also normally consists of two main blocks: the 6086 SILK encoder and the CELT encoder. However, unlike the case of the decoder, a valid 6087 (though potentially suboptimal) Opus encoder is not required to support all modes and 6088 may thus only include a SILK encoder module or a CELT encoder module. 6089 The output bit-stream of the Opus encoding contains bits from the SILK and CELT 6090 encoders, though these are not separable due to the use of a range coder. 6091 A block diagram of the encoder is illustrated below. 6092 6093 <figure align="center" anchor="opus-encoder-figure" title="Opus Encoder"> 6094 <artwork> 6095 <![CDATA[ 6096 +------------+ +---------+ 6097 | Sample | | SILK |------+ 6098 +->| Rate |--->| Encoder | V 6099 +-----------+ | | Conversion | | | +---------+ 6100 | Optional | | +------------+ +---------+ | Range | 6101 ->| High-pass |--+ | Encoder |----> 6102 | Filter | | +--------------+ +---------+ | | Bit- 6103 +-----------+ | | Delay | | CELT | +---------+ stream 6104 +->| Compensation |->| Encoder | ^ 6105 | | | |------+ 6106 +--------------+ +---------+ 6107 ]]> 6108 </artwork> 6109 </figure> 6110 </t> 6111 6112 <t> 6113 For a normal encoder where both the SILK and the CELT modules are included, an optimal 6114 encoder should select which coding mode to use at run-time depending on the conditions. 6115 In the reference implementation, the frame size is selected by the application, but the 6116 other configuration parameters (number of channels, bandwidth, mode) are automatically 6117 selected (unless explicitly overridden by the application) depend on the following: 6118 <list style="symbols"> 6119 <t>Requested bitrate</t> 6120 <t>Input sampling rate</t> 6121 <t>Type of signal (speech vs music)</t> 6122 <t>Frame size in use</t> 6123 </list> 6124 6125 The type of signal currently needs to be provided by the application (though it can be 6126 changed in real-time). An Opus encoder implementation could also do automatic detection, 6127 but since Opus is an interactive codec, such an implementation would likely have to either 6128 delay the signal (for non-interactive applications) or delay the mode switching decisions (for 6129 interactive applications). 6130 </t> 6131 6132 <t> 6133 When the encoder is configured for voice over IP applications, the input signal is 6134 filtered by a high-pass filter to remove the lowest part of the spectrum 6135 that contains little speech energy and may contain background noise. This is a second order 6136 Auto Regressive Moving Average (i.e., with poles and zeros) filter with a cut-off frequency around 50 Hz. 6137 In the future, a music detector may also be used to lower the cut-off frequency when the 6138 input signal is detected to be music rather than speech. 6139 </t> 6140 6141 <section anchor="range-encoder" title="Range Encoder"> 6142 <t> 6143 The range coder acts as the bit-packer for Opus. 6144 It is used in three different ways: to encode 6145 <list style="symbols"> 6146 <t> 6147 Entropy-coded symbols with a fixed probability model using ec_encode() 6148 (entenc.c), 6149 </t> 6150 <t> 6151 Integers from 0 to (2**M - 1) using ec_enc_uint() or ec_enc_bits() 6152 (entenc.c),</t> 6153 <t> 6154 Integers from 0 to (ft - 1) (where ft is not a power of two) using 6155 ec_enc_uint() (entenc.c). 6156 </t> 6157 </list> 6158 </t> 6159 6160 <t> 6161 The range encoder maintains an internal state vector composed of the four-tuple 6162 (val, rng, rem, ext) representing the low end of the current 6163 range, the size of the current range, a single buffered output byte, and a 6164 count of additional carry-propagating output bytes. 6165 Both val and rng are 32-bit unsigned integer values, rem is a byte value or 6166 less than 255 or the special value -1, and ext is an unsigned integer with at 6167 least 11 bits. 6168 This state vector is initialized at the start of each each frame to the value 6169 (0, 2**31, -1, 0). 6170 After encoding a sequence of symbols, the value of rng in the encoder should 6171 exactly match the value of rng in the decoder after decoding the same sequence 6172 of symbols. 6173 This is a powerful tool for detecting errors in either an encoder or decoder 6174 implementation. 6175 The value of val, on the other hand, represents different things in the encoder 6176 and decoder, and is not expected to match. 6177 </t> 6178 6179 <t> 6180 The decoder has no analog for rem and ext. 6181 These are used to perform carry propagation in the renormalization loop below. 6182 Each iteration of this loop produces 9 bits of output, consisting of 8 data 6183 bits and a carry flag. 6184 The encoder cannot determine the final value of the output bytes until it 6185 propagates these carry flags. 6186 Therefore the reference implementation buffers a single non-propagating output 6187 byte (i.e., one less than 255) in rem and keeps a count of additional 6188 propagating (i.e., 255) output bytes in ext. 6189 An implementation may choose to use any mathematically equivalent scheme to 6190 perform carry propagation. 6191 </t> 6192 6193 <section anchor="encoding-symbols" title="Encoding Symbols"> 6194 <t> 6195 The main encoding function is ec_encode() (entenc.c), which encodes symbol k in 6196 the current context using the same three-tuple (fl[k], fh[k], ft) 6197 as the decoder to describe the range of the symbol (see 6198 <xref target="range-decoder"/>). 6199 </t> 6200 <t> 6201 ec_encode() updates the state of the encoder as follows. 6202 If fl[k] is greater than zero, then 6203 <figure align="center"> 6204 <artwork align="center"><![CDATA[ 6205 rng 6206 val = val + rng - --- * (ft - fl) , 6207 ft 6208 6209 rng 6210 rng = --- * (fh - fl) . 6211 ft 6212 ]]></artwork> 6213 </figure> 6214 Otherwise, val is unchanged and 6215 <figure align="center"> 6216 <artwork align="center"><![CDATA[ 6217 rng 6218 rng = rng - --- * (fh - fl) . 6219 ft 6220 ]]></artwork> 6221 </figure> 6222 The divisions here are integer division. 6223 </t> 6224 6225 <section anchor="range-encoder-renorm" title="Renormalization"> 6226 <t> 6227 After this update, the range is normalized using a procedure very similar to 6228 that of <xref target="range-decoder-renorm"/>, implemented by 6229 ec_enc_normalize() (entenc.c). 6230 The following process is repeated until rng > 2**23. 6231 First, the top 9 bits of val, (val>>23), are sent to the carry buffer, 6232 described in <xref target="ec_enc_carry_out"/>. 6233 Then, the encoder sets 6234 <figure align="center"> 6235 <artwork align="center"><![CDATA[ 6236 val = (val<<8) & 0x7FFFFFFF , 6237 6238 rng = rng<<8 . 6239 ]]></artwork> 6240 </figure> 6241 </t> 6242 </section> 6243 6244 <section anchor="ec_enc_carry_out" 6245 title="Carry Propagation and Output Buffering"> 6246 <t> 6247 The function ec_enc_carry_out() (entenc.c) implements carry propagation and 6248 output buffering. 6249 It takes as input a 9-bit value, c, consisting of 8 data bits and an additional 6250 carry bit. 6251 If c is equal to the value 255, then ext is simply incremented, and no other 6252 state updates are performed. 6253 Otherwise, let b = (c>>8) be the carry bit. 6254 Then, 6255 <list style="symbols"> 6256 <t> 6257 If the buffered byte rem contains a value other than -1, the encoder outputs 6258 the byte (rem + b). 6259 Otherwise, if rem is -1, no byte is output. 6260 </t> 6261 <t> 6262 If ext is non-zero, then the encoder outputs ext bytes---all with a value of 0 6263 if b is set, or 255 if b is unset---and sets ext to 0. 6264 </t> 6265 <t> 6266 rem is set to the 8 data bits: 6267 <figure align="center"> 6268 <artwork align="center"><![CDATA[ 6269 rem = c & 255 . 6270 ]]></artwork> 6271 </figure> 6272 </t> 6273 </list> 6274 </t> 6275 </section> 6276 6277 </section> 6278 6279 <section anchor="encoding-alternate" title="Alternate Encoding Methods"> 6280 <t> 6281 The reference implementation uses three additional encoding methods that are 6282 exactly equivalent to the above, but make assumptions and simplifications that 6283 allow for a more efficient implementation. 6284 </t> 6285 6286 <section anchor="ec_encode_bin" title="ec_encode_bin()"> 6287 <t> 6288 The first is ec_encode_bin() (entenc.c), defined using the parameter ftb 6289 instead of ft. 6290 It is mathematically equivalent to calling ec_encode() with 6291 ft = (1<<ftb), but avoids using division. 6292 </t> 6293 </section> 6294 6295 <section anchor="ec_enc_bit_logp" title="ec_enc_bit_logp()"> 6296 <t> 6297 The next is ec_enc_bit_logp() (entenc.c), which encodes a single binary symbol. 6298 The context is described by a single parameter, logp, which is the absolute 6299 value of the base-2 logarithm of the probability of a "1". 6300 It is mathematically equivalent to calling ec_encode() with the 3-tuple 6301 (fl[k] = 0, fh[k] = (1<<logp) - 1, 6302 ft = (1<<logp)) if k is 0 and with 6303 (fl[k] = (1<<logp) - 1, 6304 fh[k] = ft = (1<<logp)) if k is 1. 6305 The implementation requires no multiplications or divisions. 6306 </t> 6307 </section> 6308 6309 <section anchor="ec_enc_icdf" title="ec_enc_icdf()"> 6310 <t> 6311 The last is ec_enc_icdf() (entenc.c), which encodes a single binary symbol with 6312 a table-based context of up to 8 bits. 6313 This uses the same icdf table as ec_dec_icdf() from 6314 <xref target="ec_dec_icdf"/>. 6315 The function is mathematically equivalent to calling ec_encode() with 6316 fl[k] = (1<<ftb) - icdf[k-1] (or 0 if 6317 k == 0), fh[k] = (1<<ftb) - icdf[k], and 6318 ft = (1<<ftb). 6319 This only saves a few arithmetic operations over ec_encode_bin(), but allows 6320 the encoder to use the same icdf tables as the decoder. 6321 </t> 6322 </section> 6323 6324 </section> 6325 6326 <section anchor="encoding-bits" title="Encoding Raw Bits"> 6327 <t> 6328 The raw bits used by the CELT layer are packed at the end of the buffer using 6329 ec_enc_bits() (entenc.c). 6330 Because the raw bits may continue into the last byte output by the range coder 6331 if there is room in the low-order bits, the encoder must be prepared to merge 6332 these values into a single byte. 6333 The procedure in <xref target="encoder-finalizing"/> does this in a way that 6334 ensures both the range coded data and the raw bits can be decoded 6335 successfully. 6336 </t> 6337 </section> 6338 6339 <section anchor="encoding-ints" title="Encoding Uniformly Distributed Integers"> 6340 <t> 6341 The function ec_enc_uint() (entenc.c) encodes one of ft equiprobable symbols in 6342 the range 0 to (ft - 1), inclusive, each with a frequency of 1, 6343 where ft may be as large as (2**32 - 1). 6344 Like the decoder (see <xref target="ec_dec_uint"/>), it splits up the 6345 value into a range coded symbol representing up to 8 of the high bits, and, if 6346 necessary, raw bits representing the remainder of the value. 6347 </t> 6348 <t> 6349 ec_enc_uint() takes a two-tuple (t, ft), where t is the value to be 6350 encoded, 0 <= t < ft, and ft is not necessarily a 6351 power of two. 6352 Let ftb = ilog(ft - 1), i.e., the number of bits required 6353 to store (ft - 1) in two's complement notation. 6354 If ftb is 8 or less, then t is encoded directly using ec_encode() with the 6355 three-tuple (t, t + 1, ft). 6356 </t> 6357 <t> 6358 If ftb is greater than 8, then the top 8 bits of t are encoded using the 6359 three-tuple (t>>(ftb - 8), 6360 (t>>(ftb - 8)) + 1, 6361 ((ft - 1)>>(ftb - 8)) + 1), and the 6362 remaining bits, 6363 (t & ((1<<(ftb - 8)) - 1), 6364 are encoded as raw bits with ec_enc_bits(). 6365 </t> 6366 </section> 6367 6368 <section anchor="encoder-finalizing" title="Finalizing the Stream"> 6369 <t> 6370 After all symbols are encoded, the stream must be finalized by outputting a 6371 value inside the current range. 6372 Let end be the integer in the interval [val, val + rng) with the 6373 largest number of trailing zero bits, b, such that 6374 (end + (1<<b) - 1) is also in the interval 6375 [val, val + rng). 6376 This choice of end allows the maximum number of trailing bits to be set to 6377 arbitrary values while still ensuring the range coded part of the buffer can 6378 be decoded correctly. 6379 Then, while end is not zero, the top 9 bits of end, i.e., (end>>23), are 6380 passed to the carry buffer in accordance with the procedure in 6381 <xref target="ec_enc_carry_out"/>, and end is updated via 6382 <figure align="center"> 6383 <artwork align="center"><![CDATA[ 6384 end = (end<<8) & 0x7FFFFFFF . 6385 ]]></artwork> 6386 </figure> 6387 Finally, if the buffered output byte, rem, is neither zero nor the special 6388 value -1, or the carry count, ext, is greater than zero, then 9 zero bits are 6389 sent to the carry buffer to flush it to the output buffer. 6390 When outputting the final byte from the range coder, if it would overlap any 6391 raw bits already packed into the end of the output buffer, they should be ORed 6392 into the same byte. 6393 The bit allocation routines in the CELT layer should ensure that this can be 6394 done without corrupting the range coder data so long as end is chosen as 6395 described above. 6396 If there is any space between the end of the range coder data and the end of 6397 the raw bits, it is padded with zero bits. 6398 This entire process is implemented by ec_enc_done() (entenc.c). 6399 </t> 6400 </section> 6401 6402 <section anchor="encoder-tell" title="Current Bit Usage"> 6403 <t> 6404 The bit allocation routines in Opus need to be able to determine a 6405 conservative upper bound on the number of bits that have been used 6406 to encode the current frame thus far. This drives allocation 6407 decisions and ensures that the range coder and raw bits will not 6408 overflow the output buffer. This is computed in the 6409 reference implementation to whole-bit precision by 6410 the function ec_tell() (entcode.h) and to fractional 1/8th bit 6411 precision by the function ec_tell_frac() (entcode.c). 6412 Like all operations in the range coder, it must be implemented in a 6413 bit-exact manner, and must produce exactly the same value returned by 6414 the same functions in the decoder after decoding the same symbols. 6415 </t> 6416 </section> 6417 6418 </section> 6419 6420 <section title='SILK Encoder'> 6421 <t> 6422 In many respects the SILK encoder mirrors the SILK decoder described 6423 in <xref target='silk_decoder_outline'/>. 6424 Details such as the quantization and range coder tables can be found 6425 there, while this section describes the high-level design choices that 6426 were made. 6427 The diagram below shows the basic modules of the SILK encoder. 6428 <figure align="center" anchor="silk_encoder_figure" title="SILK Encoder"> 6429 <artwork> 6430 <![CDATA[ 6431 +----------+ +--------+ +---------+ 6432 | Sample | | Stereo | | SILK | 6433 ------>| Rate |--->| Mixing |--->| Core |----------> 6434 Input |Conversion| | | | Encoder | Bitstream 6435 +----------+ +--------+ +---------+ 6436 ]]> 6437 </artwork> 6438 </figure> 6439 </t> 6440 6441 <section title='Sample Rate Conversion'> 6442 <t> 6443 The input signal's sampling rate is adjusted by a sample rate conversion 6444 module so that it matches the SILK internal sampling rate. 6445 The input to the sample rate converter is delayed by a number of samples 6446 depending on the sample rate ratio, such that the overall delay is constant 6447 for all input and output sample rates. 6448 </t> 6449 </section> 6450 6451 <section title='Stereo Mixing'> 6452 <t> 6453 The stereo mixer is only used for stereo input signals. 6454 It converts a stereo left/right signal into an adaptive 6455 mid/side representation. 6456 The first step is to compute non-adaptive mid/side signals 6457 as half the sum and difference between left and right signals. 6458 The side signal is then minimized in energy by subtracting a 6459 prediction of it based on the mid signal. 6460 This prediction works well when the left and right signals 6461 exhibit linear dependency, for instance for an amplitude-panned 6462 input signal. 6463 Like in the decoder, the prediction coefficients are linearly 6464 interpolated during the first 8 ms of the frame. 6465 The mid signal is always encoded, whereas the residual 6466 side signal is only encoded if it has sufficient 6467 energy compared to the mid signal's energy. 6468 If it has not, 6469 the "mid_only_flag" is set without encoding the side signal. 6470 </t> 6471 <t> 6472 The predictor coefficients are coded regardless of whether 6473 the side signal is encoded. 6474 For each frame, two predictor coefficients are computed, one 6475 that predicts between low-passed mid and side channels, and 6476 one that predicts between high-passed mid and side channels. 6477 The low-pass filter is a simple three-tap filter 6478 and creates a delay of one sample. 6479 The high-pass filtered signal is the difference between 6480 the mid signal delayed by one sample and the low-passed 6481 signal. Instead of explicitly computing the high-passed 6482 signal, it is computationally more efficient to transform 6483 the prediction coefficients before applying them to the 6484 filtered mid signal, as follows 6485 <figure align="center"> 6486 <artwork align="center"> 6487 <![CDATA[ 6488 pred(n) = LP(n) * w0 + HP(n) * w1 6489 = LP(n) * w0 + (mid(n-1) - LP(n)) * w1 6490 = LP(n) * (w0 - w1) + mid(n-1) * w1 6491 ]]> 6492 </artwork> 6493 </figure> 6494 where w0 and w1 are the low-pass and high-pass prediction 6495 coefficients, mid(n-1) is the mid signal delayed by one sample, 6496 LP(n) and HP(n) are the low-passed and high-passed 6497 signals and pred(n) is the prediction signal that is subtracted 6498 from the side signal. 6499 </t> 6500 </section> 6501 6502 <section title='SILK Core Encoder'> 6503 <t> 6504 What follows is a description of the core encoder and its components. 6505 For simplicity, the core encoder is referred to simply as the encoder in 6506 the remainder of this section. An overview of the encoder is given in 6507 <xref target="encoder_figure" />. 6508 </t> 6509 <figure align="center" anchor="encoder_figure" title="SILK Core Encoder"> 6510 <artwork align="center"> 6511 <![CDATA[ 6512 +---+ 6513 +--------------------------------->| | 6514 +---------+ | +---------+ | | 6515 |Voice | | |LTP |12 | | 6516 +-->|Activity |--+ +----->|Scaling |-----------+---->| | 6517 | |Detector |3 | | |Control |<--+ | | | 6518 | +---------+ | | +---------+ | | | | 6519 | | | +---------+ | | | | 6520 | | | |Gains | | | | | 6521 | | | +-->|Processor|---|---+---|---->| R | 6522 | | | | | |11 | | | | a | 6523 | \/ | | +---------+ | | | | n | 6524 | +---------+ | | +---------+ | | | | g | 6525 | |Pitch | | | |LSF | | | | | e | 6526 | +->|Analysis |---+ | |Quantizer|---|---|---|---->| | 6527 | | | |4 | | | |8 | | | | E |--> 6528 | | +---------+ | | +---------+ | | | | n | 2 6529 | | | | 9/\ 10| | | | | c | 6530 | | | | | \/ | | | | o | 6531 | | +---------+ | | +----------+ | | | | d | 6532 | | |Noise | +--|-->|Prediction|--+---|---|---->| e | 6533 | +->|Shaping |---|--+ |Analysis |7 | | | | r | 6534 | | |Analysis |5 | | | | | | | | | 6535 | | +---------+ | | +----------+ | | | | | 6536 | | | | /\ | | | | | 6537 | | +----------|--|--------+ | | | | | 6538 | | | \/ \/ \/ \/ \/ | | 6539 | | | +---------+ +------------+ | | 6540 | | | | | |Noise | | | 6541 -+-------+-----+------>|Prefilter|--------->|Shaping |-->| | 6542 1 | | 6 |Quantization|13 | | 6543 +---------+ +------------+ +---+ 6544 6545 1: Input speech signal 6546 2: Range encoded bitstream 6547 3: Voice activity estimate 6548 4: Pitch lags (per 5 ms) and voicing decision (per 20 ms) 6549 5: Noise shaping quantization coefficients 6550 - Short term synthesis and analysis 6551 noise shaping coefficients (per 5 ms) 6552 - Long term synthesis and analysis noise 6553 shaping coefficients (per 5 ms and for voiced speech only) 6554 - Noise shaping tilt (per 5 ms) 6555 - Quantizer gain/step size (per 5 ms) 6556 6: Input signal filtered with analysis noise shaping filters 6557 7: Short and long term prediction coefficients 6558 LTP (per 5 ms) and LPC (per 20 ms) 6559 8: LSF quantization indices 6560 9: LSF coefficients 6561 10: Quantized LSF coefficients 6562 11: Processed gains, and synthesis noise shape coefficients 6563 12: LTP state scaling coefficient. Controlling error propagation 6564 / prediction gain trade-off 6565 13: Quantized signal 6566 ]]> 6567 </artwork> 6568 </figure> 6569 6570 <section title='Voice Activity Detection'> 6571 <t> 6572 The input signal is processed by a Voice Activity Detector (VAD) to produce 6573 a measure of voice activity, spectral tilt, and signal-to-noise estimates for 6574 each frame. The VAD uses a sequence of half-band filterbanks to split the 6575 signal into four subbands: 0...Fs/16, Fs/16...Fs/8, Fs/8...Fs/4, and 6576 Fs/4...Fs/2, where Fs is the sampling frequency (8, 12, 16, or 24 kHz). 6577 The lowest subband, from 0 - Fs/16, is high-pass filtered with a first-order 6578 moving average (MA) filter (with transfer function H(z) = 1-z**(-1)) to 6579 reduce the energy at the lowest frequencies. For each frame, the signal 6580 energy per subband is computed. 6581 In each subband, a noise level estimator tracks the background noise level 6582 and a Signal-to-Noise Ratio (SNR) value is computed as the logarithm of the 6583 ratio of energy to noise level. 6584 Using these intermediate variables, the following parameters are calculated 6585 for use in other SILK modules: 6586 <list style="symbols"> 6587 <t> 6588 Average SNR. The average of the subband SNR values. 6589 </t> 6590 6591 <t> 6592 Smoothed subband SNRs. Temporally smoothed subband SNR values. 6593 </t> 6594 6595 <t> 6596 Speech activity level. Based on the average SNR and a weighted average of the 6597 subband energies. 6598 </t> 6599 6600 <t> 6601 Spectral tilt. A weighted average of the subband SNRs, with positive weights 6602 for the low subbands and negative weights for the high subbands. 6603 </t> 6604 </list> 6605 </t> 6606 </section> 6607 6608 <section title='Pitch Analysis' anchor='pitch_estimator_overview_section'> 6609 <t> 6610 The input signal is processed by the open loop pitch estimator shown in 6611 <xref target='pitch_estimator_figure' />. 6612 <figure align="center" anchor="pitch_estimator_figure" 6613 title="Block diagram of the pitch estimator"> 6614 <artwork align="center"> 6615 <![CDATA[ 6616 +--------+ +----------+ 6617 |2 x Down| |Time- | 6618 +->|sampling|->|Correlator| | 6619 | | | | | |4 6620 | +--------+ +----------+ \/ 6621 | | 2 +-------+ 6622 | | +-->|Speech |5 6623 +---------+ +--------+ | \/ | |Type |-> 6624 |LPC | |Down | | +----------+ | | 6625 +->|Analysis | +->|sample |-+------------->|Time- | +-------+ 6626 | | | | |to 8 kHz| |Correlator|-----------> 6627 | +---------+ | +--------+ |__________| 6 6628 | | | |3 6629 | \/ | \/ 6630 | +---------+ | +----------+ 6631 | |Whitening| | |Time- | 6632 -+->|Filter |-+--------------------------->|Correlator|-----------> 6633 1 | | | | 7 6634 +---------+ +----------+ 6635 6636 1: Input signal 6637 2: Lag candidates from stage 1 6638 3: Lag candidates from stage 2 6639 4: Correlation threshold 6640 5: Voiced/unvoiced flag 6641 6: Pitch correlation 6642 7: Pitch lags 6643 ]]> 6644 </artwork> 6645 </figure> 6646 The pitch analysis finds a binary voiced/unvoiced classification, and, for 6647 frames classified as voiced, four pitch lags per frame - one for each 6648 5 ms subframe - and a pitch correlation indicating the periodicity of 6649 the signal. 6650 The input is first whitened using a Linear Prediction (LP) whitening filter, 6651 where the coefficients are computed through standard Linear Prediction Coding 6652 (LPC) analysis. The order of the whitening filter is 16 for best results, but 6653 is reduced to 12 for medium complexity and 8 for low complexity modes. 6654 The whitened signal is analyzed to find pitch lags for which the time 6655 correlation is high. 6656 The analysis consists of three stages for reducing the complexity: 6657 <list style="symbols"> 6658 <t>In the first stage, the whitened signal is downsampled to 4 kHz 6659 (from 8 kHz) and the current frame is correlated to a signal delayed 6660 by a range of lags, starting from a shortest lag corresponding to 6661 500 Hz, to a longest lag corresponding to 56 Hz.</t> 6662 6663 <t> 6664 The second stage operates on an 8 kHz signal (downsampled from 12, 16, 6665 or 24 kHz) and measures time correlations only near the lags 6666 corresponding to those that had sufficiently high correlations in the first 6667 stage. The resulting correlations are adjusted for a small bias towards 6668 short lags to avoid ending up with a multiple of the true pitch lag. 6669 The highest adjusted correlation is compared to a threshold depending on: 6670 <list style="symbols"> 6671 <t> 6672 Whether the previous frame was classified as voiced 6673 </t> 6674 <t> 6675 The speech activity level 6676 </t> 6677 <t> 6678 The spectral tilt. 6679 </t> 6680 </list> 6681 If the threshold is exceeded, the current frame is classified as voiced and 6682 the lag with the highest adjusted correlation is stored for a final pitch 6683 analysis of the highest precision in the third stage. 6684 </t> 6685 <t> 6686 The last stage operates directly on the whitened input signal to compute time 6687 correlations for each of the four subframes independently in a narrow range 6688 around the lag with highest correlation from the second stage. 6689 </t> 6690 </list> 6691 </t> 6692 </section> 6693 6694 <section title='Noise Shaping Analysis' anchor='noise_shaping_analysis_overview_section'> 6695 <t> 6696 The noise shaping analysis finds gains and filter coefficients used in the 6697 prefilter and noise shaping quantizer. These parameters are chosen such that 6698 they will fulfill several requirements: 6699 <list style="symbols"> 6700 <t> 6701 Balancing quantization noise and bitrate. 6702 The quantization gains determine the step size between reconstruction levels 6703 of the excitation signal. Therefore, increasing the quantization gain 6704 amplifies quantization noise, but also reduces the bitrate by lowering 6705 the entropy of the quantization indices. 6706 </t> 6707 <t> 6708 Spectral shaping of the quantization noise; the noise shaping quantizer is 6709 capable of reducing quantization noise in some parts of the spectrum at the 6710 cost of increased noise in other parts without substantially changing the 6711 bitrate. 6712 By shaping the noise such that it follows the signal spectrum, it becomes 6713 less audible. In practice, best results are obtained by making the shape 6714 of the noise spectrum slightly flatter than the signal spectrum. 6715 </t> 6716 <t> 6717 De-emphasizing spectral valleys; by using different coefficients in the 6718 analysis and synthesis part of the prefilter and noise shaping quantizer, 6719 the levels of the spectral valleys can be decreased relative to the levels 6720 of the spectral peaks such as speech formants and harmonics. 6721 This reduces the entropy of the signal, which is the difference between the 6722 coded signal and the quantization noise, thus lowering the bitrate. 6723 </t> 6724 <t> 6725 Matching the levels of the decoded speech formants to the levels of the 6726 original speech formants; an adjustment gain and a first order tilt 6727 coefficient are computed to compensate for the effect of the noise 6728 shaping quantization on the level and spectral tilt. 6729 </t> 6730 </list> 6731 </t> 6732 <t> 6733 <figure align="center" anchor="noise_shape_analysis_spectra_figure" 6734 title="Noise shaping and spectral de-emphasis illustration"> 6735 <artwork align="center"> 6736 <![CDATA[ 6737 / \ ___ 6738 | // \\ 6739 | // \\ ____ 6740 |_// \\___// \\ ____ 6741 | / ___ \ / \\ // \\ 6742 P |/ / \ \_/ \\_____// \\ 6743 o | / \ ____ \ / \\ 6744 w | / \___/ \ \___/ ____ \\___ 1 6745 e |/ \ / \ \ 6746 r | \_____/ \ \__ 2 6747 | \ 6748 | \___ 3 6749 | 6750 +----------------------------------------> 6751 Frequency 6752 6753 1: Input signal spectrum 6754 2: De-emphasized and level matched spectrum 6755 3: Quantization noise spectrum 6756 ]]> 6757 </artwork> 6758 </figure> 6759 <xref target='noise_shape_analysis_spectra_figure' /> shows an example of an 6760 input signal spectrum (1). 6761 After de-emphasis and level matching, the spectrum has deeper valleys (2). 6762 The quantization noise spectrum (3) more or less follows the input signal 6763 spectrum, while having slightly less pronounced peaks. 6764 The entropy, which provides a lower bound on the bitrate for encoding the 6765 excitation signal, is proportional to the area between the de-emphasized 6766 spectrum (2) and the quantization noise spectrum (3). Without de-emphasis, 6767 the entropy is proportional to the area between input spectrum (1) and 6768 quantization noise (3) - clearly higher. 6769 </t> 6770 6771 <t> 6772 The transformation from input signal to de-emphasized signal can be 6773 described as a filtering operation with a filter 6774 <figure align="center"> 6775 <artwork align="center"> 6776 <![CDATA[ 6777 -1 Wana(z) 6778 H(z) = G * ( 1 - c_tilt * z ) * ------- 6779 Wsyn(z), 6780 ]]> 6781 </artwork> 6782 </figure> 6783 having an adjustment gain G, a first order tilt adjustment filter with 6784 tilt coefficient c_tilt, and where 6785 <figure align="center"> 6786 <artwork align="center"> 6787 <![CDATA[ 6788 16 d 6789 __ -k -L __ -k 6790 Wana(z) = (1 - \ (a_ana(k) * z )*(1 - z * \ b_ana(k) * z ), 6791 /_ /_ 6792 k=1 k=-d 6793 ]]> 6794 </artwork> 6795 </figure> 6796 is the analysis part of the de-emphasis filter, consisting of the short-term 6797 shaping filter with coefficients a_ana(k), and the long-term shaping filter 6798 with coefficients b_ana(k) and pitch lag L. 6799 The parameter d determines the number of long-term shaping filter taps. 6800 </t> 6801 6802 <t> 6803 Similarly, but without the tilt adjustment, the synthesis part can be written as 6804 <figure align="center"> 6805 <artwork align="center"> 6806 <![CDATA[ 6807 16 d 6808 __ -k -L __ -k 6809 Wsyn(z) = (1 - \ (a_syn(k) * z )*(1 - z * \ b_syn(k) * z ). 6810 /_ /_ 6811 k=1 k=-d 6812 ]]> 6813 </artwork> 6814 </figure> 6815 </t> 6816 <t> 6817 All noise shaping parameters are computed and applied per subframe of 5 ms. 6818 First, an LPC analysis is performed on a windowed signal block of 15 ms. 6819 The signal block has a look-ahead of 5 ms relative to the current subframe, 6820 and the window is an asymmetric sine window. The LPC analysis is done with the 6821 autocorrelation method, with an order of between 8, in lowest-complexity mode, 6822 and 16, for best quality. 6823 </t> 6824 <t> 6825 Optionally the LPC analysis and noise shaping filters are warped by replacing 6826 the delay elements by first-order allpass filters. 6827 This increases the frequency resolution at low frequencies and reduces it at 6828 high ones, which better matches the human auditory system and improves 6829 quality. 6830 The warped analysis and filtering comes at a cost in complexity 6831 and is therefore only done in higher complexity modes. 6832 </t> 6833 <t> 6834 The quantization gain is found by taking the square root of the residual energy 6835 from the LPC analysis and multiplying it by a value inversely proportional 6836 to the coding quality control parameter and the pitch correlation. 6837 </t> 6838 <t> 6839 Next the two sets of short-term noise shaping coefficients a_ana(k) and 6840 a_syn(k) are obtained by applying different amounts of bandwidth expansion to the 6841 coefficients found in the LPC analysis. 6842 This bandwidth expansion moves the roots of the LPC polynomial towards the 6843 origin, using the formulas 6844 <figure align="center"> 6845 <artwork align="center"> 6846 <![CDATA[ 6847 k 6848 a_ana(k) = a(k)*g_ana , and 6849 6850 k 6851 a_syn(k) = a(k)*g_syn , 6852 ]]> 6853 </artwork> 6854 </figure> 6855 where a(k) is the k'th LPC coefficient, and the bandwidth expansion factors 6856 g_ana and g_syn are calculated as 6857 <figure align="center"> 6858 <artwork align="center"> 6859 <![CDATA[ 6860 g_ana = 0.95 - 0.01*C, and 6861 6862 g_syn = 0.95 + 0.01*C, 6863 ]]> 6864 </artwork> 6865 </figure> 6866 where C is the coding quality control parameter between 0 and 1. 6867 Applying more bandwidth expansion to the analysis part than to the synthesis 6868 part gives the desired de-emphasis of spectral valleys in between formants. 6869 </t> 6870 6871 <t> 6872 The long-term shaping is applied only during voiced frames. 6873 It uses three filter taps, described by 6874 <figure align="center"> 6875 <artwork align="center"> 6876 <![CDATA[ 6877 b_ana = F_ana * [0.25, 0.5, 0.25], and 6878 6879 b_syn = F_syn * [0.25, 0.5, 0.25]. 6880 ]]> 6881 </artwork> 6882 </figure> 6883 For unvoiced frames these coefficients are set to 0. The multiplication factors 6884 F_ana and F_syn are chosen between 0 and 1, depending on the coding quality 6885 control parameter, as well as the calculated pitch correlation and smoothed 6886 subband SNR of the lowest subband. By having F_ana less than F_syn, 6887 the pitch harmonics are emphasized relative to the valleys in between the 6888 harmonics. 6889 </t> 6890 6891 <t> 6892 The tilt coefficient c_tilt is for unvoiced frames chosen as 6893 <figure align="center"> 6894 <artwork align="center"> 6895 <![CDATA[ 6896 c_tilt = 0.25, 6897 ]]> 6898 </artwork> 6899 </figure> 6900 and as 6901 <figure align="center"> 6902 <artwork align="center"> 6903 <![CDATA[ 6904 c_tilt = 0.25 + 0.2625 * V 6905 ]]> 6906 </artwork> 6907 </figure> 6908 for voiced frames, where V is the voice activity level between 0 and 1. 6909 </t> 6910 <t> 6911 The adjustment gain G serves to correct any level mismatch between the original 6912 and decoded signals that might arise from the noise shaping and de-emphasis. 6913 This gain is computed as the ratio of the prediction gain of the short-term 6914 analysis and synthesis filter coefficients. The prediction gain of an LPC 6915 synthesis filter is the square root of the output energy when the filter is 6916 excited by a unit-energy impulse on the input. 6917 An efficient way to compute the prediction gain is by first computing the 6918 reflection coefficients from the LPC coefficients through the step-down 6919 algorithm, and extracting the prediction gain from the reflection coefficients 6920 as 6921 <figure align="center"> 6922 <artwork align="center"> 6923 <![CDATA[ 6924 K 6925 ___ 2 -0.5 6926 predGain = ( | | 1 - (r_k) ) , 6927 k=1 6928 ]]> 6929 </artwork> 6930 </figure> 6931 where r_k is the k'th reflection coefficient. 6932 </t> 6933 6934 <t> 6935 Initial values for the quantization gains are computed as the square-root of 6936 the residual energy of the LPC analysis, adjusted by the coding quality control 6937 parameter. 6938 These quantization gains are later adjusted based on the results of the 6939 prediction analysis. 6940 </t> 6941 </section> 6942 6943 <section title='Prediction Analysis' anchor='pred_ana_overview_section'> 6944 <t> 6945 The prediction analysis is performed in one of two ways depending on how 6946 the pitch estimator classified the frame. 6947 The processing for voiced and unvoiced speech is described in 6948 <xref target='pred_ana_voiced_overview_section' /> and 6949 <xref target='pred_ana_unvoiced_overview_section' />, respectively. 6950 Inputs to this function include the pre-whitened signal from the 6951 pitch estimator (see <xref target='pitch_estimator_overview_section'/>). 6952 </t> 6953 6954 <section title='Voiced Speech' anchor='pred_ana_voiced_overview_section'> 6955 <t> 6956 For a frame of voiced speech the pitch pulses will remain dominant in the 6957 pre-whitened input signal. 6958 Further whitening is desirable as it leads to higher quality at the same 6959 available bitrate. 6960 To achieve this, a Long-Term Prediction (LTP) analysis is carried out to 6961 estimate the coefficients of a fifth-order LTP filter for each of four 6962 subframes. 6963 The LTP coefficients are quantized using the method described in 6964 <xref target='ltp_quantizer_overview_section'/>, and the quantized LTP 6965 coefficients are used to compute the LTP residual signal. 6966 This LTP residual signal is the input to an LPC analysis where the LPC coefficients are 6967 estimated using Burg's method <xref target="Burg"/>, such that the residual energy is minimized. 6968 The estimated LPC coefficients are converted to a Line Spectral Frequency (LSF) vector 6969 and quantized as described in <xref target='lsf_quantizer_overview_section'/>. 6970 After quantization, the quantized LSF vector is converted back to LPC 6971 coefficients using the full procedure in <xref target="silk_nlsfs"/>. 6972 By using quantized LTP coefficients and LPC coefficients derived from the 6973 quantized LSF coefficients, the encoder remains fully synchronized with the 6974 decoder. 6975 The quantized LPC and LTP coefficients are also used to filter the input 6976 signal and measure residual energy for each of the four subframes. 6977 </t> 6978 </section> 6979 <section title='Unvoiced Speech' anchor='pred_ana_unvoiced_overview_section'> 6980 <t> 6981 For a speech signal that has been classified as unvoiced, there is no need 6982 for LTP filtering, as it has already been determined that the pre-whitened 6983 input signal is not periodic enough within the allowed pitch period range 6984 for LTP analysis to be worth the cost in terms of complexity and bitrate. 6985 The pre-whitened input signal is therefore discarded, and instead the input 6986 signal is used for LPC analysis using Burg's method. 6987 The resulting LPC coefficients are converted to an LSF vector and quantized 6988 as described in the following section. 6989 They are then transformed back to obtain quantized LPC coefficients, which 6990 are then used to filter the input signal and measure residual energy for 6991 each of the four subframes. 6992 </t> 6993 <section title="Burg's Method"> 6994 <t> 6995 The main purpose of linear prediction in SILK is to reduce the bitrate by 6996 minimizing the residual energy. 6997 At least at high bitrates, perceptual aspects are handled 6998 independently by the noise shaping filter. 6999 Burg's method is used because it provides higher prediction gain 7000 than the autocorrelation method and, unlike the covariance method, 7001 produces stable filters (assuming numerical errors don't spoil 7002 that). SILK's implementation of Burg's method is also computationally 7003 faster than the autocovariance method. 7004 The implementation of Burg's method differs from traditional 7005 implementations in two aspects. 7006 The first difference is that it 7007 operates on autocorrelations, similar to the Schur algorithm <xref target="Schur"/>, but 7008 with a simple update to the autocorrelations after finding each 7009 reflection coefficient to make the result identical to Burg's method. 7010 This brings down the complexity of Burg's method to near that of 7011 the autocorrelation method. 7012 The second difference is that the signal in each subframe is scaled 7013 by the inverse of the residual quantization step size. Subframes with 7014 a small quantization step size will on average spend more bits for a 7015 given amount of residual energy than subframes with a large step size. 7016 Without scaling, Burg's method minimizes the total residual energy in 7017 all subframes, which doesn't necessarily minimize the total number of 7018 bits needed for coding the quantized residual. The residual energy 7019 of the scaled subframes is a better measure for that number of 7020 bits. 7021 </t> 7022 </section> 7023 </section> 7024 </section> 7025 7026 <section title='LSF Quantization' anchor='lsf_quantizer_overview_section'> 7027 <t> 7028 Unlike many other speech codecs, SILK uses variable bitrate coding 7029 for the LSFs. 7030 This improves the average rate-distortion (R-D) tradeoff and reduces outliers. 7031 The variable bitrate coding minimizes a linear combination of the weighted 7032 quantization errors and the bitrate. 7033 The weights for the quantization errors are the Inverse 7034 Harmonic Mean Weighting (IHMW) function proposed by Laroia et al. 7035 (see <xref target="laroia-icassp" />). 7036 These weights are referred to here as Laroia weights. 7037 </t> 7038 <t> 7039 The LSF quantizer consists of two stages. 7040 The first stage is an (unweighted) vector quantizer (VQ), with a 7041 codebook size of 32 vectors. 7042 The quantization errors for the codebook vector are sorted, and 7043 for the N best vectors a second stage quantizer is run. 7044 By varying the number N a tradeoff is made between R-D performance 7045 and computational efficiency. 7046 For each of the N codebook vectors the Laroia weights corresponding 7047 to that vector (and not to the input vector) are calculated. 7048 Then the residual between the input LSF vector and the codebook 7049 vector is scaled by the square roots of these Laroia weights. 7050 This scaling partially normalizes error sensitivity for the 7051 residual vector, so that a uniform quantizer with fixed 7052 step sizes can be used in the second stage without too much 7053 performance loss. 7054 And by scaling with Laroia weights determined from the first-stage 7055 codebook vector, the process can be reversed in the decoder. 7056 </t> 7057 <t> 7058 The second stage uses predictive delayed decision scalar 7059 quantization. 7060 The quantization error is weighted by Laroia weights determined 7061 from the LSF input vector. 7062 The predictor multiplies the previous quantized residual value 7063 by a prediction coefficient that depends on the vector index from the 7064 first stage VQ and on the location in the LSF vector. 7065 The prediction is subtracted from the LSF residual value before 7066 quantizing the result, and added back afterwards. 7067 This subtraction can be interpreted as shifting the quantization levels 7068 of the scalar quantizer, and as a result the quantization error of 7069 each value depends on the quantization decision of the previous value. 7070 This dependency is exploited by the delayed decision mechanism to 7071 search for a quantization sequency with best R-D performance 7072 with a Viterbi-like algorithm <xref target="Viterbi"/>. 7073 The quantizer processes the residual LSF vector in reverse order 7074 (i.e., it starts with the highest residual LSF value). 7075 This is done because the prediction works slightly 7076 better in the reverse direction. 7077 </t> 7078 <t> 7079 The quantization index of the first stage is entropy coded. 7080 The quantization sequence from the second stage is also entropy 7081 coded, where for each element the probability table is chosen 7082 depending on the vector index from the first stage and the location 7083 of that element in the LSF vector. 7084 </t> 7085 7086 <section title='LSF Stabilization' anchor='lsf_stabilizer_overview_section'> 7087 <t> 7088 If the input is stable, finding the best candidate usually results in a 7089 quantized vector that is also stable. Because of the two-stage approach, 7090 however, it is possible that the best quantization candidate is unstable. 7091 The encoder applies the same stabilization procedure applied by the decoder 7092 (see <xref target="silk_nlsf_stabilization"/> to ensure the LSF parameters 7093 are within their valid range, increasingly sorted, and have minimum 7094 distances between each other and the border values. 7095 </t> 7096 </section> 7097 </section> 7098 7099 <section title='LTP Quantization' anchor='ltp_quantizer_overview_section'> 7100 <t> 7101 For voiced frames, the prediction analysis described in 7102 <xref target='pred_ana_voiced_overview_section' /> resulted in four sets 7103 (one set per subframe) of five LTP coefficients, plus four weighting matrices. 7104 The LTP coefficients for each subframe are quantized using entropy constrained 7105 vector quantization. 7106 A total of three vector codebooks are available for quantization, with 7107 different rate-distortion trade-offs. The three codebooks have 10, 20, and 7108 40 vectors and average rates of about 3, 4, and 5 bits per vector, respectively. 7109 Consequently, the first codebook has larger average quantization distortion at 7110 a lower rate, whereas the last codebook has smaller average quantization 7111 distortion at a higher rate. 7112 Given the weighting matrix W_ltp and LTP vector b, the weighted rate-distortion 7113 measure for a codebook vector cb_i with rate r_i is give by 7114 <figure align="center"> 7115 <artwork align="center"> 7116 <![CDATA[ 7117 RD = u * (b - cb_i)' * W_ltp * (b - cb_i) + r_i, 7118 ]]> 7119 </artwork> 7120 </figure> 7121 where u is a fixed, heuristically-determined parameter balancing the distortion 7122 and rate. 7123 Which codebook gives the best performance for a given LTP vector depends on the 7124 weighting matrix for that LTP vector. 7125 For example, for a low valued W_ltp, it is advantageous to use the codebook 7126 with 10 vectors as it has a lower average rate. 7127 For a large W_ltp, on the other hand, it is often better to use the codebook 7128 with 40 vectors, as it is more likely to contain the best codebook vector. 7129 The weighting matrix W_ltp depends mostly on two aspects of the input signal. 7130 The first is the periodicity of the signal; the more periodic, the larger W_ltp. 7131 The second is the change in signal energy in the current subframe, relative to 7132 the signal one pitch lag earlier. 7133 A decaying energy leads to a larger W_ltp than an increasing energy. 7134 Both aspects fluctuate relatively slowly, which causes the W_ltp matrices for 7135 different subframes of one frame often to be similar. 7136 Because of this, one of the three codebooks typically gives good performance 7137 for all subframes, and therefore the codebook search for the subframe LTP 7138 vectors is constrained to only allow codebook vectors to be chosen from the 7139 same codebook, resulting in a rate reduction. 7140 </t> 7141 7142 <t> 7143 To find the best codebook, each of the three vector codebooks is 7144 used to quantize all subframe LTP vectors and produce a combined 7145 weighted rate-distortion measure for each vector codebook. 7146 The vector codebook with the lowest combined rate-distortion 7147 over all subframes is chosen. The quantized LTP vectors are used 7148 in the noise shaping quantizer, and the index of the codebook 7149 plus the four indices for the four subframe codebook vectors 7150 are passed on to the range encoder. 7151 </t> 7152 </section> 7153 7154 <section title='Prefilter'> 7155 <t> 7156 In the prefilter the input signal is filtered using the spectral valley 7157 de-emphasis filter coefficients from the noise shaping analysis 7158 (see <xref target='noise_shaping_analysis_overview_section'/>). 7159 By applying only the noise shaping analysis filter to the input signal, 7160 it provides the input to the noise shaping quantizer. 7161 </t> 7162 </section> 7163 7164 <section title='Noise Shaping Quantizer'> 7165 <t> 7166 The noise shaping quantizer independently shapes the signal and coding noise 7167 spectra to obtain a perceptually higher quality at the same bitrate. 7168 </t> 7169 <t> 7170 The prefilter output signal is multiplied with a compensation gain G computed 7171 in the noise shaping analysis. Then the output of a synthesis shaping filter 7172 is added, and the output of a prediction filter is subtracted to create a 7173 residual signal. 7174 The residual signal is multiplied by the inverse quantized quantization gain 7175 from the noise shaping analysis, and input to a scalar quantizer. 7176 The quantization indices of the scalar quantizer represent a signal of pulses 7177 that is input to the pyramid range encoder. 7178 The scalar quantizer also outputs a quantization signal, which is multiplied 7179 by the quantized quantization gain from the noise shaping analysis to create 7180 an excitation signal. 7181 The output of the prediction filter is added to the excitation signal to form 7182 the quantized output signal y(n). 7183 The quantized output signal y(n) is input to the synthesis shaping and 7184 prediction filters. 7185 </t> 7186 <t> 7187 Optionally the noise shaping quantizer operates in a delayed decision 7188 mode. 7189 In this mode it uses a Viterbi algorithm to keep track of 7190 multiple rounding choices in the quantizer and select the best 7191 one after a delay of 32 samples. This improves the rate/distortion 7192 performance of the quantizer. 7193 </t> 7194 </section> 7195 7196 <section title='Constant Bitrate Mode'> 7197 <t> 7198 SILK was designed to run in Variable Bitrate (VBR) mode. However 7199 the reference implementation also has a Constant Bitrate (CBR) mode 7200 for SILK. In CBR mode SILK will attempt to encode each packet with 7201 no more than the allowed number of bits. The Opus wrapper code 7202 then pads the bitstream if any unused bits are left in SILK mode, or 7203 encodes the high band with the remaining number of bits in Hybrid mode. 7204 The number of payload bits is adjusted by changing 7205 the quantization gains and the rate/distortion tradeoff in the noise 7206 shaping quantizer, in an iterative loop 7207 around the noise shaping quantizer and entropy coding. 7208 Compared to the SILK VBR mode, the CBR mode has lower 7209 audio quality at a given average bitrate, and also has higher 7210 computational complexity. 7211 </t> 7212 </section> 7213 7214 </section> 7215 7216 </section> 7217 7218 7219 <section title="CELT Encoder"> 7220 <t> 7221 Most of the aspects of the CELT encoder can be directly derived from the description 7222 of the decoder. For example, the filters and rotations in the encoder are simply the 7223 inverse of the operation performed by the decoder. Similarly, the quantizers generally 7224 optimize for the mean square error (because noise shaping is part of the bit-stream itself), 7225 so no special search is required. For this reason, only the less straightforward aspects of the 7226 encoder are described here. 7227 </t> 7228 7229 <section anchor="pitch-prefilter" title="Pitch Prefilter"> 7230 <t>The pitch prefilter is applied after the pre-emphasis. It is applied 7231 in such a way as to be the inverse of the decoder's post-filter. The main non-obvious aspect of the 7232 prefilter is the selection of the pitch period. The pitch search should be optimized for the 7233 following criteria: 7234 <list style="symbols"> 7235 <t>continuity: it is important that the pitch period 7236 does not change abruptly between frames; and</t> 7237 <t>avoidance of pitch multiples: when the period used is a multiple of the real period 7238 (lower frequency fundamental), the post-filter loses most of its ability to reduce noise</t> 7239 </list> 7240 </t> 7241 </section> 7242 7243 <section anchor="normalization" title="Bands and Normalization"> 7244 <t> 7245 The MDCT output is divided into bands that are designed to match the ear's critical 7246 bands for the smallest (2.5 ms) frame size. The larger frame sizes use integer 7247 multiples of the 2.5 ms layout. For each band, the encoder 7248 computes the energy that will later be encoded. Each band is then normalized by the 7249 square root of the <spanx style="strong">unquantized</spanx> energy, such that each band now forms a unit vector X. 7250 The energy and the normalization are computed by compute_band_energies() 7251 and normalise_bands() (bands.c), respectively. 7252 </t> 7253 </section> 7254 7255 <section anchor="energy-quantization" title="Energy Envelope Quantization"> 7256 7257 <t> 7258 Energy quantization (both coarse and fine) can be easily understood from the decoding process. 7259 For all useful bitrates, the coarse quantizer always chooses the quantized log energy value that 7260 minimizes the error for each band. Only at very low rate does the encoder allow larger errors to 7261 minimize the rate and avoid using more bits than are available. When the 7262 available CPU requirements allow it, it is best to try encoding the coarse energy both with and without 7263 inter-frame prediction such that the best prediction mode can be selected. The optimal mode depends on 7264 the coding rate, the available bitrate, and the current rate of packet loss. 7265 </t> 7266 7267 <t>The fine energy quantizer always chooses the quantized log energy value that 7268 minimizes the error for each band because the rate of the fine quantization depends only 7269 on the bit allocation and not on the values that are coded. 7270 </t> 7271 </section> <!-- Energy quant --> 7272 7273 <section title="Bit Allocation"> 7274 <t>The encoder must use exactly the same bit allocation process as used by the decoder 7275 and described in <xref target="allocation"/>. The three mechanisms that can be used by the 7276 encoder to adjust the bitrate on a frame-by-frame basis are band boost, allocation trim, 7277 and band skipping. 7278 </t> 7279 7280 <section title="Band Boost"> 7281 <t>The reference encoder makes a decision to boost a band when the energy of that band is significantly 7282 higher than that of the neighboring bands. Let E_j be the log-energy of band j, we define 7283 <list> 7284 <t>D_j = 2*E_j - E_j-1 - E_j+1 </t> 7285 </list> 7286 7287 The allocation of band j is boosted once if D_j > t1 and twice if D_j > t2. For LM>=1, t1=2 and t2=4, 7288 while for LM<1, t1=3 and t2=5. 7289 </t> 7290 7291 </section> 7292 7293 <section title="Allocation Trim"> 7294 <t>The allocation trim is a value between 0 and 10 (inclusively) that controls the allocation 7295 balance between the low and high frequencies. The encoder starts with a safe "default" of 5 7296 and deviates from that default in two different ways. First the trim can deviate by +/- 2 7297 depending on the spectral tilt of the input signal. For signals with more low frequencies, the 7298 trim is increased by up to 2, while for signals with more high frequencies, the trim is 7299 decreased by up to 2. 7300 For stereo inputs, the trim value can 7301 be decreased by up to 4 when the inter-channel correlation at low frequency (first 8 bands) 7302 is high. </t> 7303 </section> 7304 7305 <section title="Band Skipping"> 7306 <t>The encoder uses band skipping to ensure that the shape of the bands is only coded 7307 if there is at least 1/2 bit per sample available for the PVQ. If not, then no bit is allocated 7308 and folding is used instead. To ensure continuity in the allocation, some amount of hysteresis is 7309 added to the process, such that a band that received PVQ bits in the previous frame only needs 7/16 7310 bit/sample to be coded for the current frame, while a band that did not receive PVQ bits in the 7311 previous frames needs at least 9/16 bit/sample to be coded.</t> 7312 </section> 7313 7314 </section> 7315 7316 <section title="Stereo Decisions"> 7317 <t>Because CELT applies mid-side stereo coupling in the normalized domain, it does not suffer from 7318 important stereo image problems even when the two channels are completely uncorrelated. For this reason 7319 it is always safe to use stereo coupling on any audio frame. That being said, there are some frames 7320 for which dual (independent) stereo is still more efficient. This decision is made by comparing the estimated 7321 entropy with and without coupling over the first 13 bands, taking into account the fact that all bands with 7322 more than two MDCT bins require one extra degree of freedom when coded in mid-side. Let L1_ms and L1_lr 7323 be the L1-norm of the mid-side vector and the L1-norm of the left-right vector, respectively. The decision 7324 to use mid-side is made if and only if 7325 <figure align="center"> 7326 <artwork align="center"><![CDATA[ 7327 L1_ms L1_lr 7328 -------- < ----- 7329 bins + E bins 7330 ]]></artwork> 7331 </figure> 7332 where bins is the number of MDCT bins in the first 13 bands and E is the number of extra degrees of 7333 freedom for mid-side coding. For LM>1, E=13, otherwise E=5. 7334 </t> 7335 7336 <t>The reference encoder decides on the intensity stereo threshold based on the bitrate alone. After 7337 taking into account the frame size by subtracting 80 bits per frame for coarse energy, the first 7338 band using intensity coding is as follows: 7339 </t> 7340 7341 <texttable anchor="intensity-thresholds" 7342 title="Thresholds for Intensity Stereo"> 7343 <ttcol align='center'>bitrate (kb/s)</ttcol> 7344 <ttcol align='center'>start band</ttcol> 7345 <c><35</c> <c>8</c> 7346 <c>35-50</c> <c>12</c> 7347 <c>50-68</c> <c>16</c> 7348 <c>84-84</c> <c>18</c> 7349 <c>84-102</c> <c>19</c> 7350 <c>102-130</c> <c>20</c> 7351 <c>>130</c> <c>disabled</c> 7352 </texttable> 7353 7354 7355 </section> 7356 7357 <section title="Time-Frequency Decision"> 7358 <t> 7359 The choice of time-frequency resolution used in <xref target="tf-change"></xref> is based on 7360 R-D optimization. The distortion is the L1-norm (sum of absolute values) of each band 7361 after each TF resolution under consideration. The L1 norm is used because it represents the entropy 7362 for a Laplacian source. The number of bits required to code a change in TF resolution between 7363 two bands is higher than the cost of having those two bands use the same resolution, which is 7364 what requires the R-D optimization. The optimal decision is computed using the Viterbi algorithm. 7365 See tf_analysis() in celt/celt.c. 7366 </t> 7367 </section> 7368 7369 <section title="Spreading Values Decision"> 7370 <t> 7371 The choice of the spreading value in <xref target="spread values"></xref> has an 7372 impact on the nature of the coding noise introduced by CELT. The larger the f_r value, the 7373 lower the impact of the rotation, and the more tonal the coding noise. The 7374 more tonal the signal, the more tonal the noise should be, so the CELT encoder determines 7375 the optimal value for f_r by estimating how tonal the signal is. The tonality estimate 7376 is based on discrete pdf (4-bin histogram) of each band. Bands that have a large number of small 7377 values are considered more tonal and a decision is made by combining all bands with more than 7378 8 samples. See spreading_decision() in celt/bands.c. 7379 </t> 7380 </section> 7381 7382 <section anchor="pvq" title="Spherical Vector Quantization"> 7383 <t>CELT uses a Pyramid Vector Quantization (PVQ) <xref target="PVQ"></xref> 7384 codebook for quantizing the details of the spectrum in each band that have not 7385 been predicted by the pitch predictor. The PVQ codebook consists of all sums 7386 of K signed pulses in a vector of N samples, where two pulses at the same position 7387 are required to have the same sign. Thus the codebook includes 7388 all integer codevectors y of N dimensions that satisfy sum(abs(y(j))) = K. 7389 </t> 7390 7391 <t> 7392 In bands where there are sufficient bits allocated PVQ is used to encode 7393 the unit vector that results from the normalization in 7394 <xref target="normalization"></xref> directly. Given a PVQ codevector y, 7395 the unit vector X is obtained as X = y/||y||, where ||.|| denotes the 7396 L2 norm. 7397 </t> 7398 7399 7400 <section anchor="pvq-search" title="PVQ Search"> 7401 7402 <t> 7403 The search for the best codevector y is performed by alg_quant() 7404 (vq.c). There are several possible approaches to the 7405 search, with a trade-off between quality and complexity. The method used in the reference 7406 implementation computes an initial codeword y1 by projecting the normalized spectrum 7407 X onto the codebook pyramid of K-1 pulses: 7408 </t> 7409 <t> 7410 y0 = truncate_towards_zero( (K-1) * X / sum(abs(X))) 7411 </t> 7412 7413 <t> 7414 Depending on N, K and the input data, the initial codeword y0 may contain from 7415 0 to K-1 non-zero values. All the remaining pulses, with the exception of the last one, 7416 are found iteratively with a greedy search that minimizes the normalized correlation 7417 between y and X: 7418 <figure align="center"> 7419 <artwork align="center"><![CDATA[ 7420 T 7421 J = -X * y / ||y|| 7422 ]]></artwork> 7423 </figure> 7424 </t> 7425 7426 <t> 7427 The search described above is considered to be a good trade-off between quality 7428 and computational cost. However, there are other possible ways to search the PVQ 7429 codebook and the implementers MAY use any other search methods. See alg_quant() in celt/vq.c. 7430 </t> 7431 </section> 7432 7433 <section anchor="cwrs-encoder" title="PVQ Encoding"> 7434 7435 <t> 7436 The vector to encode, X, is converted into an index i such that 7437 0 <= i < V(N,K) as follows. 7438 Let i = 0 and k = 0. 7439 Then for j = (N - 1) down to 0, inclusive, do: 7440 <list style="numbers"> 7441 <t> 7442 If k > 0, set 7443 i = i + (V(N-j-1,k-1) + V(N-j,k-1))/2. 7444 </t> 7445 <t>Set k = k + abs(X[j]).</t> 7446 <t> 7447 If X[j] < 0, set 7448 i = i + (V(N-j-1,k) + V(N-j,k))/2. 7449 </t> 7450 </list> 7451 </t> 7452 7453 <t> 7454 The index i is then encoded using the procedure in 7455 <xref target="encoding-ints"/> with ft = V(N,K). 7456 </t> 7457 7458 </section> 7459 7460 </section> 7461 7462 7463 7464 7465 7466 </section> 7467 7468 </section> 7469 7470 7471 <section anchor="conformance" title="Conformance"> 7472 7473 <t> 7474 It is our intention to allow the greatest possible choice of freedom in 7475 implementing the specification. For this reason, outside of the exceptions 7476 noted in this section, conformance is defined through the reference 7477 implementation of the decoder provided in <xref target="ref-implementation"/>. 7478 Although this document includes an English description of the codec, should 7479 the description contradict the source code of the reference implementation, 7480 the latter shall take precedence. 7481 </t> 7482 7483 <t> 7484 Compliance with this specification means that in addition to following the normative keywords in this document, 7485 a decoder's output MUST also be 7486 within the thresholds specified by the opus_compare.c tool (included 7487 with the code) when compared to the reference implementation for each of the 7488 test vectors provided (see <xref target="test-vectors"></xref>) and for each output 7489 sampling rate and channel count supported. In addition, a compliant 7490 decoder implementation MUST have the same final range decoder state as that of the 7491 reference decoder. It is therefore RECOMMENDED that the 7492 decoder implement the same functional behavior as the reference. 7493 7494 A decoder implementation is not required to support all output sampling 7495 rates or all output channel counts. 7496 </t> 7497 7498 <section title="Testing"> 7499 <t> 7500 Using the reference code provided in <xref target="ref-implementation"></xref>, 7501 a test vector can be decoded with 7502 <list> 7503 <t>opus_demo -d <rate> <channels> testvectorX.bit testX.out</t> 7504 </list> 7505 where <rate> is the sampling rate and can be 8000, 12000, 16000, 24000, or 48000, and 7506 <channels> is 1 for mono or 2 for stereo. 7507 </t> 7508 7509 <t> 7510 If the range decoder state is incorrect for one of the frames, the decoder will exit with 7511 "Error: Range coder state mismatch between encoder and decoder". If the decoder succeeds, then 7512 the output can be compared with the "reference" output with 7513 <list> 7514 <t>opus_compare -s -r <rate> testvectorX.dec testX.out</t> 7515 </list> 7516 for stereo or 7517 <list> 7518 <t>opus_compare -r <rate> testvectorX.dec testX.out</t> 7519 </list> 7520 for mono. 7521 </t> 7522 7523 <t>In addition to indicating whether the test vector comparison passes, the opus_compare tool 7524 outputs an "Opus quality metric" that indicates how well the tested decoder matches the 7525 reference implementation. A quality of 0 corresponds to the passing threshold, while 7526 a quality of 100 is the highest possible value and means that the output of the tested decoder is identical to the reference 7527 implementation. The passing threshold (quality 0) was calibrated in such a way that it corresponds to 7528 additive white noise with a 48 dB SNR (similar to what can be obtained on a cassette deck). 7529 It is still possible for an implementation to sound very good with such a low quality measure 7530 (e.g. if the deviation is due to inaudible phase distortion), but unless this is verified by 7531 listening tests, it is RECOMMENDED that implementations achieve a quality above 90 for 48 kHz 7532 decoding. For other sampling rates, it is normal for the quality metric to be lower 7533 (typically as low as 50 even for a good implementation) because of harmless mismatch with 7534 the delay and phase of the internal sampling rate conversion. 7535 </t> 7536 7537 <t> 7538 On POSIX environments, the run_vectors.sh script can be used to verify all test 7539 vectors. This can be done with 7540 <list> 7541 <t>run_vectors.sh <exec path> <vector path> <rate></t> 7542 </list> 7543 where <exec path> is the directory where the opus_demo and opus_compare executables 7544 are built and <vector path> is the directory containing the test vectors. 7545 </t> 7546 </section> 7547 7548 <section anchor="opus-custom" title="Opus Custom"> 7549 <t> 7550 Opus Custom is an OPTIONAL part of the specification that is defined to 7551 handle special sample rates and frame rates that are not supported by the 7552 main Opus specification. Use of Opus Custom is discouraged for all but very 7553 special applications for which a frame size different from 2.5, 5, 10, or 20 ms is 7554 needed (for either complexity or latency reasons). Because Opus Custom is 7555 optional, streams encoded using Opus Custom cannot be expected to be decodable by all Opus 7556 implementations. Also, because no in-band mechanism exists for specifying the sampling 7557 rate and frame size of Opus Custom streams, out-of-band signaling is required. 7558 In Opus Custom operation, only the CELT layer is available, using the opus_custom_* function 7559 calls in opus_custom.h. 7560 </t> 7561 </section> 7562 7563 </section> 7564 7565 <section anchor="security" title="Security Considerations"> 7566 7567 <t> 7568 Implementations of the Opus codec need to take appropriate security considerations 7569 into account, as outlined in <xref target="DOS"/>. 7570 It is extremely important for the decoder to be robust against malicious 7571 payloads. 7572 Malicious payloads must not cause the decoder to overrun its allocated memory 7573 or to take an excessive amount of resources to decode. 7574 Although problems 7575 in encoders are typically rarer, the same applies to the encoder. Malicious 7576 audio streams must not cause the encoder to misbehave because this would 7577 allow an attacker to attack transcoding gateways. 7578 </t> 7579 <t> 7580 The reference implementation contains no known buffer overflow or cases where 7581 a specially crafted packet or audio segment could cause a significant increase 7582 in CPU load. 7583 However, on certain CPU architectures where denormalized floating-point 7584 operations are much slower than normal floating-point operations, it is 7585 possible for some audio content (e.g., silence or near-silence) to cause an 7586 increase in CPU load. 7587 Denormals can be introduced by reordering operations in the compiler and depend 7588 on the target architecture, so it is difficult to guarantee that an implementation 7589 avoids them. 7590 For architectures on which denormals are problematic, adding very small 7591 floating-point offsets to the affected signals to prevent significant numbers 7592 of denormalized operations is RECOMMENDED. 7593 Alternatively, it is often possible to configure the hardware to treat 7594 denormals as zero (DAZ). 7595 No such issue exists for the fixed-point reference implementation. 7596 </t> 7597 <t>The reference implementation was validated in the following conditions: 7598 <list style="numbers"> 7599 <t> 7600 Sending the decoder valid packets generated by the reference encoder and 7601 verifying that the decoder's final range coder state matches that of the 7602 encoder. 7603 </t> 7604 <t> 7605 Sending the decoder packets generated by the reference encoder and then 7606 subjected to random corruption. 7607 </t> 7608 <t>Sending the decoder random packets.</t> 7609 <t> 7610 Sending the decoder packets generated by a version of the reference encoder 7611 modified to make random coding decisions (internal fuzzing), including mode 7612 switching, and verifying that the range coder final states match. 7613 </t> 7614 </list> 7615 In all of the conditions above, both the encoder and the decoder were run 7616 inside the <xref target="Valgrind">Valgrind</xref> memory 7617 debugger, which tracks reads and writes to invalid memory regions as well as 7618 the use of uninitialized memory. 7619 There were no errors reported on any of the tested conditions. 7620 </t> 7621 </section> 7622 7623 7624 <section title="IANA Considerations"> 7625 <t> 7626 This document has no actions for IANA. 7627 </t> 7628 </section> 7629 7630 <section anchor="Acknowledgements" title="Acknowledgements"> 7631 <t> 7632 Thanks to all other developers, including Raymond Chen, Soeren Skak Jensen, Gregory Maxwell, 7633 Christopher Montgomery, and Karsten Vandborg Soerensen. We would also 7634 like to thank Igor Dyakonov, Jan Skoglund, and Christian Hoene for their help with subjective testing of the 7635 Opus codec. Thanks to Ralph Giles, John Ridges, Ben Schwartz, Keith Yan, Christian Hoene, Kat Walsh, and many others on the Opus and CELT mailing lists 7636 for their bug reports and feedback. 7637 </t> 7638 </section> 7639 7640 <section title="Copying Conditions"> 7641 <t>The authors agree to grant third parties the irrevocable right to copy, use and distribute 7642 the work (excluding Code Components available under the simplified BSD license), with or 7643 without modification, in any medium, without royalty, provided that, unless separate 7644 permission is granted, redistributed modified works do not contain misleading author, version, 7645 name of work, or endorsement information.</t> 7646 </section> 7647 7648 </middle> 7649 7650 <back> 7651 7652 <references title="Normative References"> 7653 7654 <reference anchor="rfc2119"> 7655 <front> 7656 <title>Key words for use in RFCs to Indicate Requirement Levels </title> 7657 <author initials="S." surname="Bradner" fullname="Scott Bradner"></author> 7658 </front> 7659 <seriesInfo name="RFC" value="2119" /> 7660 </reference> 7661 7662 </references> 7663 7664 <references title="Informative References"> 7665 7666 <reference anchor='requirements'> 7667 <front> 7668 <title>Requirements for an Internet Audio Codec</title> 7669 <author initials='J.-M.' surname='Valin' fullname='J.-M. Valin'> 7670 <organization /></author> 7671 <author initials='K.' surname='Vos' fullname='K. Vos'> 7672 <organization /></author> 7673 <author> 7674 <organization>IETF</organization></author> 7675 <date year='2011' month='August' /> 7676 <abstract> 7677 <t>This document provides specific requirements for an Internet audio 7678 codec. These requirements address quality, sample rate, bitrate, 7679 and packet-loss robustness, as well as other desirable properties. 7680 </t></abstract></front> 7681 <seriesInfo name='RFC' value='6366' /> 7682 <format type='TXT' target='http://tools.ietf.org/rfc/rfc6366.txt' /> 7683 </reference> 7684 7685 <?rfc include="http://xml.resource.org/public/rfc/bibxml/reference.RFC.3550.xml"?> 7686 <?rfc include="http://xml.resource.org/public/rfc/bibxml/reference.RFC.3533.xml"?> 7687 7688 <reference anchor='SILK' target='http://developer.skype.com/silk'> 7689 <front> 7690 <title>SILK Speech Codec</title> 7691 <author initials='K.' surname='Vos' fullname='K. 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Soerensen'> 7696 <organization /></author> 7697 <date year='2010' month='March' /> 7698 <abstract> 7699 <t></t> 7700 </abstract></front> 7701 <seriesInfo name='Internet-Draft' value='draft-vos-silk-01' /> 7702 <format type='TXT' target='http://tools.ietf.org/html/draft-vos-silk-01' /> 7703 </reference> 7704 7705 <reference anchor="laroia-icassp"> 7706 <front> 7707 <title abbrev="Robust and Efficient Quantization of Speech LSP"> 7708 Robust and Efficient Quantization of Speech LSP Parameters Using Structured Vector Quantization 7709 </title> 7710 <author initials="R.L." surname="Laroia" fullname="R."> 7711 <organization/> 7712 </author> 7713 <author initials="N.P." surname="Phamdo" fullname="N."> 7714 <organization/> 7715 </author> 7716 <author initials="N.F." surname="Farvardin" fullname="N."> 7717 <organization/> 7718 </author> 7719 </front> 7720 <seriesInfo name="ICASSP-1991, Proc. IEEE Int. Conf. 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Burg"><organization/></author> 7943 </front> 7944 </reference> 7945 7946 <reference anchor="Schur"> 7947 <front> 7948 <title>A fixed point computation of partial correlation coefficients</title> 7949 <author initials="J." surname="Le Roux" fullname="J. Le Roux"><organization/></author> 7950 <author initials="C." surname="Gueguen" fullname="C. Gueguen"><organization/></author> 7951 </front> 7952 <seriesInfo name="ICASSP-1977, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, pp. 257-259, October" value="1977"/> 7953 </reference> 7954 7955 <reference anchor="Princen86"> 7956 <front> 7957 <title>Analysis/synthesis filter bank design based on time domain aliasing cancellation</title> 7958 <author initials="J." surname="Princen" fullname="John P. Princen"><organization/></author> 7959 <author initials="A." surname="Bradley" fullname="Alan B. Bradley"><organization/></author> 7960 </front> 7961 <seriesInfo name="IEEE Trans. Acoust. Speech Sig. Proc. ASSP-34 (5), 1153-1161" value="1986"/> 7962 </reference> 7963 7964 <reference anchor="Valin2010"> 7965 <front> 7966 <title>A High-Quality Speech and Audio Codec With Less Than 10 ms delay</title> 7967 <author initials="JM" surname="Valin" fullname="Jean-Marc Valin"><organization/> 7968 </author> 7969 <author initials="T. B." surname="Terriberry" fullname="Timothy Terriberry"><organization/></author> 7970 <author initials="C." surname="Montgomery" fullname="Christopher Montgomery"><organization/></author> 7971 <author initials="G." surname="Maxwell" fullname="Gregory Maxwell"><organization/></author> 7972 </front> 7973 <seriesInfo name="IEEE Trans. on Audio, Speech and Language Processing, Vol. 18, No. 1, pp. 58-67" value="2010" /> 7974 </reference> 7975 7976 7977 <reference anchor="Zwicker61"> 7978 <front> 7979 <title>Subdivision of the audible frequency range into critical bands</title> 7980 <author initials="E." surname="Zwicker" fullname="E. Zwicker"><organization/></author> 7981 <date month="February" year="1961" /> 7982 </front> 7983 <seriesInfo name="The Journal of the Acoustical Society of America, Vol. 33, No 2" value="p. 248" /> 7984 </reference> 7985 7986 7987 </references> 7988 7989 <section anchor="ref-implementation" title="Reference Implementation"> 7990 7991 <t>This appendix contains the complete source code for the 7992 reference implementation of the Opus codec written in C. By default, 7993 this implementation relies on floating-point arithmetic, but it can be 7994 compiled to use only fixed-point arithmetic by defining the FIXED_POINT 7995 macro. Information on building and using the reference implementation is 7996 available in the README file. 7997 </t> 7998 7999 <t>The implementation can be compiled with either a C89 or a C99 8000 compiler. It is reasonably optimized for most platforms such that 8001 only architecture-specific optimizations are likely to be useful. 8002 The FFT <xref target="FFT"/> used is a slightly modified version of the KISS-FFT library, 8003 but it is easy to substitute any other FFT library. 8004 </t> 8005 8006 <t> 8007 While the reference implementation does not rely on any 8008 <spanx style="emph">undefined behavior</spanx> as defined by C89 or C99, 8009 it relies on common <spanx style="emph">implementation-defined behavior</spanx> 8010 for two's complement architectures: 8011 <list style="symbols"> 8012 <t>Right shifts of negative values are consistent with two's complement arithmetic, so that a>>b is equivalent to floor(a/(2**b)),</t> 8013 <t>For conversion to a signed integer of N bits, the value is reduced modulo 2**N to be within range of the type,</t> 8014 <t>The result of integer division of a negative value is truncated towards zero, and</t> 8015 <t>The compiler provides a 64-bit integer type (a C99 requirement which is supported by most C89 compilers).</t> 8016 </list> 8017 </t> 8018 8019 <t> 8020 In its current form, the reference implementation also requires the following 8021 architectural characteristics to obtain acceptable performance: 8022 <list style="symbols"> 8023 <t>Two's complement arithmetic,</t> 8024 <t>At least a 16 bit by 16 bit integer multiplier (32-bit result), and</t> 8025 <t>At least a 32-bit adder/accumulator.</t> 8026 </list> 8027 </t> 8028 8029 8030 <section title="Extracting the source"> 8031 <t> 8032 The complete source code can be extracted from this draft, by running the 8033 following command line: 8034 8035 <list style="symbols"> 8036 <t><![CDATA[ 8037 cat draft-ietf-codec-opus.txt | grep '^\ \ \ ###' | sed -e 's/...###//' | base64 -d > opus_source.tar.gz 8038 ]]></t> 8039 <t> 8040 tar xzvf opus_source.tar.gz 8041 </t> 8042 <t>cd opus_source</t> 8043 <t>make</t> 8044 </list> 8045 On systems where the provided Makefile does not work, the following command line may be used to compile 8046 the source code: 8047 <list style="symbols"> 8048 <t><![CDATA[ 8049 cc -O2 -g -o opus_demo src/opus_demo.c `cat *.mk | grep -v fixed | sed -e 's/.*=//' -e 's/\\\\//'` -DOPUS_BUILD -Iinclude -Icelt -Isilk -Isilk/float -DUSE_ALLOCA -Drestrict= -lm 8050 ]]></t></list> 8051 </t> 8052 8053 <t> 8054 On systems where the base64 utility is not present, the following commands can be used instead: 8055 <list style="symbols"> 8056 <t><![CDATA[ 8057 cat draft-ietf-codec-opus.txt | grep '^\ \ \ ###' | sed -e 's/...###//' > opus.b64 8058 ]]></t> 8059 <t>openssl base64 -d -in opus.b64 > opus_source.tar.gz</t> 8060 </list> 8061 8062 </t> 8063 </section> 8064 8065 <section title="Up-to-date Implementation"> 8066 <t> 8067 As of the time of publication of this memo, an up-to-date implementation conforming to 8068 this standard is available in a 8069 <xref target='Opus-git'>Git repository</xref>. 8070 Releases and other resources are available at 8071 <xref target='Opus-website'/>. However, although that implementation is expected to 8072 remain conformant with the standard, it is the code in this document that shall 8073 remain normative. 8074 </t> 8075 </section> 8076 8077 <section title="Base64-encoded Source Code"> 8078 <t> 8079 <?rfc include="opus_source.base64"?> 8080 </t> 8081 </section> 8082 8083 <section anchor="test-vectors" title="Test Vectors"> 8084 <t> 8085 Because of size constraints, the Opus test vectors are not distributed in this 8086 draft. They are available in the proceedings of the 83th IETF meeting (Paris) <xref target="Vectors-proc"/> and from the Opus codec website at 8087 <xref target="Vectors-website"/>. These test vectors were created specifically to exercise 8088 all aspects of the decoder and therefore the audio quality of the decoded output is 8089 significantly lower than what Opus can achieve in normal operation. 8090 </t> 8091 8092 <t> 8093 The SHA1 hash of the files in the test vector package are 8094 <?rfc include="testvectors_sha1"?> 8095 </t> 8096 8097 </section> 8098 8099 </section> 8100 8101 <section anchor="self-delimiting-framing" title="Self-Delimiting Framing"> 8102 <t> 8103 To use the internal framing described in <xref target="modes"/>, the decoder 8104 must know the total length of the Opus packet, in bytes. 8105 This section describes a simple variation of that framing which can be used 8106 when the total length of the packet is not known. 8107 Nothing in the encoding of the packet itself allows a decoder to distinguish 8108 between the regular, undelimited framing and the self-delimiting framing 8109 described in this appendix. 8110 Which one is used and where must be established by context at the transport 8111 layer. 8112 It is RECOMMENDED that a transport layer choose exactly one framing scheme, 8113 rather than allowing an encoder to signal which one it wants to use. 8114 </t> 8115 8116 <t> 8117 For example, although a regular Opus stream does not support more than two 8118 channels, a multi-channel Opus stream may be formed from several one- and 8119 two-channel streams. 8120 To pack an Opus packet from each of these streams together in a single packet 8121 at the transport layer, one could use the self-delimiting framing for all but 8122 the last stream, and then the regular, undelimited framing for the last one. 8123 Reverting to the undelimited framing for the last stream saves overhead 8124 (because the total size of the transport-layer packet will still be known), 8125 and ensures that a "multi-channel" stream which only has a single Opus stream 8126 uses the same framing as a regular Opus stream does. 8127 This avoids the need for signaling to distinguish these two cases. 8128 </t> 8129 8130 <t> 8131 The self-delimiting framing is identical to the regular, undelimited framing 8132 from <xref target="modes"/>, except that each Opus packet contains one extra 8133 length field, encoded using the same one- or two-byte scheme from 8134 <xref target="frame-length-coding"/>. 8135 This extra length immediately precedes the compressed data of the first Opus 8136 frame in the packet, and is interpreted in the various modes as follows: 8137 <list style="symbols"> 8138 <t> 8139 Code 0 packets: It is the length of the single Opus frame (see 8140 <xref target="sd_code0_packet"/>). 8141 </t> 8142 <t> 8143 Code 1 packets: It is the length used for both of the Opus frames (see 8144 <xref target="sd_code1_packet"/>). 8145 </t> 8146 <t> 8147 Code 2 packets: It is the length of the second Opus frame (see 8148 <xref target="sd_code2_packet"/>).</t> 8149 <t> 8150 CBR Code 3 packets: It is the length used for all of the Opus frames (see 8151 <xref target="sd_code3cbr_packet"/>). 8152 </t> 8153 <t>VBR Code 3 packets: It is the length of the last Opus frame (see 8154 <xref target="sd_code3vbr_packet"/>). 8155 </t> 8156 </list> 8157 </t> 8158 8159 <figure anchor="sd_code0_packet" title="A Self-Delimited Code 0 Packet" 8160 align="center"> 8161 <artwork align="center"><![CDATA[ 8162 0 1 2 3 8163 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 8164 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8165 | config |s|0|0| N1 (1-2 bytes): | 8166 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | 8167 | Compressed frame 1 (N1 bytes)... : 8168 : | 8169 | | 8170 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8171 ]]></artwork> 8172 </figure> 8173 8174 <figure anchor="sd_code1_packet" title="A Self-Delimited Code 1 Packet" 8175 align="center"> 8176 <artwork align="center"><![CDATA[ 8177 0 1 2 3 8178 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 8179 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8180 | config |s|0|1| N1 (1-2 bytes): | 8181 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ : 8182 | Compressed frame 1 (N1 bytes)... | 8183 : +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8184 | | | 8185 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ : 8186 | Compressed frame 2 (N1 bytes)... | 8187 : +-+-+-+-+-+-+-+-+ 8188 | | 8189 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8190 ]]></artwork> 8191 </figure> 8192 8193 <figure anchor="sd_code2_packet" title="A Self-Delimited Code 2 Packet" 8194 align="center"> 8195 <artwork align="center"><![CDATA[ 8196 0 1 2 3 8197 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 8198 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8199 | config |s|1|0| N1 (1-2 bytes): N2 (1-2 bytes : | 8200 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ : 8201 | Compressed frame 1 (N1 bytes)... | 8202 : +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8203 | | | 8204 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | 8205 | Compressed frame 2 (N2 bytes)... : 8206 : | 8207 | | 8208 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8209 ]]></artwork> 8210 </figure> 8211 8212 <figure anchor="sd_code3cbr_packet" title="A Self-Delimited CBR Code 3 Packet" 8213 align="center"> 8214 <artwork align="center"><![CDATA[ 8215 0 1 2 3 8216 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 8217 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8218 | config |s|1|1|0|p| M | Pad len (Opt) : N1 (1-2 bytes): 8219 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8220 | | 8221 : Compressed frame 1 (N1 bytes)... : 8222 | | 8223 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8224 | | 8225 : Compressed frame 2 (N1 bytes)... : 8226 | | 8227 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8228 | | 8229 : ... : 8230 | | 8231 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8232 | | 8233 : Compressed frame M (N1 bytes)... : 8234 | | 8235 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8236 : Opus Padding (Optional)... | 8237 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8238 ]]></artwork> 8239 </figure> 8240 8241 <figure anchor="sd_code3vbr_packet" title="A Self-Delimited VBR Code 3 Packet" 8242 align="center"> 8243 <artwork align="center"><![CDATA[ 8244 0 1 2 3 8245 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 8246 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8247 | config |s|1|1|1|p| M | Padding length (Optional) : 8248 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8249 : N1 (1-2 bytes): ... : N[M-1] | N[M] : 8250 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8251 | | 8252 : Compressed frame 1 (N1 bytes)... : 8253 | | 8254 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8255 | | 8256 : Compressed frame 2 (N2 bytes)... : 8257 | | 8258 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8259 | | 8260 : ... : 8261 | | 8262 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8263 | | 8264 : Compressed frame M (N[M] bytes)... : 8265 | | 8266 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8267 : Opus Padding (Optional)... | 8268 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 8269 ]]></artwork> 8270 </figure> 8271 8272 </section> 8273 8274 </back> 8275 8276 </rfc> 8277
