release/src/router/libvorbis/doc/06-floor0.tex

   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