1 % -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*- 2 %!TEX root = Vorbis_I_spec.tex 3 % $Id$ 4 \section{Floor type 0 setup and decode} \label{vorbis:spec:floor0} 5 6 \subsection{Overview} 7 8 Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately 9 known as Line Spectral Frequency or LSF) representation to encode a 10 smooth spectral envelope curve as the frequency response of the LSP 11 filter. This representation is equivalent to a traditional all-pole 12 infinite impulse response filter as would be used in linear predictive 13 coding; LSP representation may be converted to LPC representation and 14 vice-versa. 15 16 17 18 \subsection{Floor 0 format} 19 20 Floor zero configuration consists of six integer fields and a list of 21 VQ codebooks for use in coding/decoding the LSP filter coefficient 22 values used by each frame. 23 24 \subsubsection{header decode} 25 26 Configuration information for instances of floor zero decodes from the 27 codec setup header (third packet). configuration decode proceeds as 28 follows: 29 30 \begin{Verbatim}[commandchars=\\\{\}] 31 1) [floor0_order] = read an unsigned integer of 8 bits 32 2) [floor0_rate] = read an unsigned integer of 16 bits 33 3) [floor0_bark_map_size] = read an unsigned integer of 16 bits 34 4) [floor0_amplitude_bits] = read an unsigned integer of six bits 35 5) [floor0_amplitude_offset] = read an unsigned integer of eight bits 36 6) [floor0_number_of_books] = read an unsigned integer of four bits and add 1 37 7) array [floor0_book_list] = read a list of [floor0_number_of_books] unsigned integers of eight bits each; 38 \end{Verbatim} 39 40 An end-of-packet condition during any of these bitstream reads renders 41 this stream undecodable. In addition, any element of the array 42 \varname{[floor0_book_list]} that is greater than the maximum codebook 43 number for this bitstream is an error condition that also renders the 44 stream undecodable. 45 46 47 48 \subsubsection{packet decode} \label{vorbis:spec:floor0-decode} 49 50 Extracting a floor0 curve from an audio packet consists of first 51 decoding the curve amplitude and \varname{[floor0_order]} LSP 52 coefficient values from the bitstream, and then computing the floor 53 curve, which is defined as the frequency response of the decoded LSP 54 filter. 55 56 Packet decode proceeds as follows: 57 \begin{Verbatim}[commandchars=\\\{\}] 58 1) [amplitude] = read an unsigned integer of [floor0_amplitude_bits] bits 59 2) if ( [amplitude] is greater than zero ) \{ 60 3) [coefficients] is an empty, zero length vector 61 4) [booknumber] = read an unsigned integer of \link{vorbis:spec:ilog}{ilog}( [floor0_number_of_books] ) bits 62 5) if ( [booknumber] is greater than the highest number decode codebook ) then packet is undecodable 63 6) [last] = zero; 64 7) vector [temp_vector] = read vector from bitstream using codebook number [floor0_book_list] element [booknumber] in VQ context. 65 8) add the scalar value [last] to each scalar in vector [temp_vector] 66 9) [last] = the value of the last scalar in vector [temp_vector] 67 10) concatenate [temp_vector] onto the end of the [coefficients] vector 68 11) if (length of vector [coefficients] is less than [floor0_order], continue at step 6 69 70 \} 71 72 12) done. 73 74 \end{Verbatim} 75 76 Take note of the following properties of decode: 77 \begin{itemize} 78 \item An \varname{[amplitude]} value of zero must result in a return code that indicates this channel is unused in this frame (the output of the channel will be all-zeroes in synthesis). Several later stages of decode don't occur for an unused channel. 79 \item An end-of-packet condition during decode should be considered a 80 nominal occruence; if end-of-packet is reached during any read 81 operation above, floor decode is to return 'unused' status as if the 82 \varname{[amplitude]} value had read zero at the beginning of decode. 83 84 \item The book number used for decode 85 can, in fact, be stored in the bitstream in \link{vorbis:spec:ilog}{ilog}( \varname{[floor0_number_of_books]} - 86 1 ) bits. Nevertheless, the above specification is correct and values 87 greater than the maximum possible book value are reserved. 88 89 \item The number of scalars read into the vector \varname{[coefficients]} 90 may be greater than \varname{[floor0_order]}, the number actually 91 required for curve computation. For example, if the VQ codebook used 92 for the floor currently being decoded has a 93 \varname{[codebook_dimensions]} value of three and 94 \varname{[floor0_order]} is ten, the only way to fill all the needed 95 scalars in \varname{[coefficients]} is to to read a total of twelve 96 scalars as four vectors of three scalars each. This is not an error 97 condition, and care must be taken not to allow a buffer overflow in 98 decode. The extra values are not used and may be ignored or discarded. 99 \end{itemize} 100 101 102 103 104 \subsubsection{curve computation} \label{vorbis:spec:floor0-synth} 105 106 Given an \varname{[amplitude]} integer and \varname{[coefficients]} 107 vector from packet decode as well as the [floor0_order], 108 [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits] and 109 [floor0_amplitude_offset] values from floor setup, and an output 110 vector size \varname{[n]} specified by the decode process, we compute a 111 floor output vector. 112 113 If the value \varname{[amplitude]} is zero, the return value is a 114 length \varname{[n]} vector with all-zero scalars. Otherwise, begin by 115 assuming the following definitions for the given vector to be 116 synthesized: 117 118 \begin{displaymath} 119 \mathrm{map}_i = \left\{ 120 \begin{array}{ll} 121 \min ( 122 \mathtt{floor0\_bark\_map\_size} - 1, 123 foobar 124 ) & \textrm{for } i \in [0,n-1] \\ 125 -1 & \textrm{for } i = n 126 \end{array} 127 \right. 128 \end{displaymath} 129 130 where 131 132 \begin{displaymath} 133 foobar = 134 \left\lfloor 135 \mathrm{bark}\left(\frac{\mathtt{floor0\_rate} \cdot i}{2n}\right) \cdot \frac{\mathtt{floor0\_bark\_map\_size}} {\mathrm{bark}(.5 \cdot \mathtt{floor0\_rate})} 136 \right\rfloor 137 \end{displaymath} 138 139 and 140 141 \begin{displaymath} 142 \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2 + .0001x) 143 \end{displaymath} 144 145 The above is used to synthesize the LSP curve on a Bark-scale frequency 146 axis, then map the result to a linear-scale frequency axis. 147 Similarly, the below calculation synthesizes the output LSP curve \varname{[output]} on a log 148 (dB) amplitude scale, mapping it to linear amplitude in the last step: 149 150 \begin{enumerate} 151 \item \varname{[i]} = 0 152 \item \varname{[$\omega$]} = $\pi$ * map element \varname{[i]} / \varname{[floor0_bark_map_size]} 153 \item if ( \varname{[floor0_order]} is odd ) { 154 \begin{enumerate} 155 \item calculate \varname{[p]} and \varname{[q]} according to: 156 \begin{eqnarray*} 157 p & = & (1 - \cos^2\omega)\prod_{j=0}^{\frac{\mathtt{floor0\_order}-3}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\ 158 q & = & \frac{1}{4} \prod_{j=0}^{\frac{\mathtt{floor0\_order}-1}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2 159 \end{eqnarray*} 160 161 \end{enumerate} 162 } else \varname{[floor0_order]} is even { 163 \begin{enumerate} 164 \item calculate \varname{[p]} and \varname{[q]} according to: 165 \begin{eqnarray*} 166 p & = & \frac{(1 - \cos^2\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\_order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\ 167 q & = & \frac{(1 + \cos^2\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\_order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2 168 \end{eqnarray*} 169 170 \end{enumerate} 171 } 172 173 \item calculate \varname{[linear_floor_value]} according to: 174 \begin{displaymath} 175 \exp \left( .11512925 \left(\frac{\mathtt{amplitude} \cdot \mathtt{floor0\_amplitute\_offset}}{(2^{\mathtt{floor0\_amplitude\_bits}}-1)\sqrt{p+q}} 176 - \mathtt{floor0\_amplitude\_offset} \right) \right) 177 \end{displaymath} 178 179 \item \varname{[iteration_condition]} = map element \varname{[i]} 180 \item \varname{[output]} element \varname{[i]} = \varname{[linear_floor_value]} 181 \item increment \varname{[i]} 182 \item if ( map element \varname{[i]} is equal to \varname{[iteration_condition]} ) continue at step 5 183 \item if ( \varname{[i]} is less than \varname{[n]} ) continue at step 2 184 \item done 185 \end{enumerate} 186 187 188 189 190 191 192 193
