mirror of
https://github.com/cookiengineer/audacity
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193 lines
8.3 KiB
TeX
193 lines
8.3 KiB
TeX
% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-
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%!TEX root = Vorbis_I_spec.tex
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% $Id$
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\section{Floor type 0 setup and decode} \label{vorbis:spec:floor0}
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\subsection{Overview}
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Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately
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known as Line Spectral Frequency or LSF) representation to encode a
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smooth spectral envelope curve as the frequency response of the LSP
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filter. This representation is equivalent to a traditional all-pole
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infinite impulse response filter as would be used in linear predictive
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coding; LSP representation may be converted to LPC representation and
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vice-versa.
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\subsection{Floor 0 format}
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Floor zero configuration consists of six integer fields and a list of
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VQ codebooks for use in coding/decoding the LSP filter coefficient
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values used by each frame.
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\subsubsection{header decode}
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Configuration information for instances of floor zero decodes from the
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codec setup header (third packet). configuration decode proceeds as
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follows:
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\begin{Verbatim}[commandchars=\\\{\}]
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1) [floor0\_order] = read an unsigned integer of 8 bits
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2) [floor0\_rate] = read an unsigned integer of 16 bits
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3) [floor0\_bark\_map\_size] = read an unsigned integer of 16 bits
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4) [floor0\_amplitude\_bits] = read an unsigned integer of six bits
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5) [floor0\_amplitude\_offset] = read an unsigned integer of eight bits
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6) [floor0\_number\_of\_books] = read an unsigned integer of four bits and add 1
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7) array [floor0\_book\_list] = read a list of [floor0\_number\_of\_books] unsigned integers of eight bits each;
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\end{Verbatim}
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An end-of-packet condition during any of these bitstream reads renders
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this stream undecodable. In addition, any element of the array
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\varname{[floor0\_book\_list]} that is greater than the maximum codebook
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number for this bitstream is an error condition that also renders the
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stream undecodable.
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\subsubsection{packet decode} \label{vorbis:spec:floor0-decode}
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Extracting a floor0 curve from an audio packet consists of first
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decoding the curve amplitude and \varname{[floor0\_order]} LSP
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coefficient values from the bitstream, and then computing the floor
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curve, which is defined as the frequency response of the decoded LSP
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filter.
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Packet decode proceeds as follows:
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\begin{Verbatim}[commandchars=\\\{\}]
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1) [amplitude] = read an unsigned integer of [floor0\_amplitude\_bits] bits
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2) if ( [amplitude] is greater than zero ) \{
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3) [coefficients] is an empty, zero length vector
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4) [booknumber] = read an unsigned integer of \link{vorbis:spec:ilog}{ilog}( [floor0\_number\_of\_books] ) bits
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5) if ( [booknumber] is greater than the highest number decode codebook ) then packet is undecodable
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6) [last] = zero;
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7) vector [temp\_vector] = read vector from bitstream using codebook number [floor0\_book\_list] element [booknumber] in VQ context.
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8) add the scalar value [last] to each scalar in vector [temp\_vector]
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9) [last] = the value of the last scalar in vector [temp\_vector]
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10) concatenate [temp\_vector] onto the end of the [coefficients] vector
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11) if (length of vector [coefficients] is less than [floor0\_order], continue at step 6
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\}
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12) done.
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\end{Verbatim}
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Take note of the following properties of decode:
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\begin{itemize}
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\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.
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\item An end-of-packet condition during decode should be considered a
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nominal occruence; if end-of-packet is reached during any read
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operation above, floor decode is to return 'unused' status as if the
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\varname{[amplitude]} value had read zero at the beginning of decode.
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\item The book number used for decode
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can, in fact, be stored in the bitstream in \link{vorbis:spec:ilog}{ilog}( \varname{[floor0\_number\_of\_books]} -
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1 ) bits. Nevertheless, the above specification is correct and values
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greater than the maximum possible book value are reserved.
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\item The number of scalars read into the vector \varname{[coefficients]}
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may be greater than \varname{[floor0\_order]}, the number actually
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required for curve computation. For example, if the VQ codebook used
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for the floor currently being decoded has a
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\varname{[codebook\_dimensions]} value of three and
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\varname{[floor0\_order]} is ten, the only way to fill all the needed
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scalars in \varname{[coefficients]} is to to read a total of twelve
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scalars as four vectors of three scalars each. This is not an error
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condition, and care must be taken not to allow a buffer overflow in
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decode. The extra values are not used and may be ignored or discarded.
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\end{itemize}
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\subsubsection{curve computation} \label{vorbis:spec:floor0-synth}
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Given an \varname{[amplitude]} integer and \varname{[coefficients]}
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vector from packet decode as well as the [floor0\_order],
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[floor0\_rate], [floor0\_bark\_map\_size], [floor0\_amplitude\_bits] and
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[floor0\_amplitude\_offset] values from floor setup, and an output
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vector size \varname{[n]} specified by the decode process, we compute a
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floor output vector.
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If the value \varname{[amplitude]} is zero, the return value is a
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length \varname{[n]} vector with all-zero scalars. Otherwise, begin by
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assuming the following definitions for the given vector to be
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synthesized:
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\begin{displaymath}
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\mathrm{map}_i = \left\{
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\begin{array}{ll}
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\min (
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\mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size} - 1,
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foobar
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) & \textrm{for } i \in [0,n-1] \\
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-1 & \textrm{for } i = n
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\end{array}
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\right.
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\end{displaymath}
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where
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\begin{displaymath}
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foobar =
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\left\lfloor
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\mathrm{bark}\left(\frac{\mathtt{floor0\texttt{\_}rate} \cdot i}{2n}\right) \cdot \frac{\mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size}} {\mathrm{bark}(.5 \cdot \mathtt{floor0\texttt{\_}rate})}
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\right\rfloor
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\end{displaymath}
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and
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\begin{displaymath}
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\mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2 + .0001x)
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\end{displaymath}
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The above is used to synthesize the LSP curve on a Bark-scale frequency
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axis, then map the result to a linear-scale frequency axis.
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Similarly, the below calculation synthesizes the output LSP curve \varname{[output]} on a log
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(dB) amplitude scale, mapping it to linear amplitude in the last step:
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\begin{enumerate}
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\item \varname{[i]} = 0
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\item \varname{[$\omega$]} = $\pi$ * map element \varname{[i]} / \varname{[floor0\_bark\_map\_size]}
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\item if ( \varname{[floor0\_order]} is odd ) {
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\begin{enumerate}
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\item calculate \varname{[p]} and \varname{[q]} according to:
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\begin{eqnarray*}
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p & = & (1 - \cos^2\omega)\prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-3}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\
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q & = & \frac{1}{4} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-1}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
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\end{eqnarray*}
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\end{enumerate}
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} else \varname{[floor0\_order]} is even {
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\begin{enumerate}[resume]
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\item calculate \varname{[p]} and \varname{[q]} according to:
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\begin{eqnarray*}
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p & = & \frac{(1 - \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\
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q & = & \frac{(1 + \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
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\end{eqnarray*}
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\end{enumerate}
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}
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\item calculate \varname{[linear\_floor\_value]} according to:
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\begin{displaymath}
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\exp \left( .11512925 \left(\frac{\mathtt{amplitude} \cdot \mathtt{floor0\texttt{\_}amplitute\texttt{\_}offset}}{(2^{\mathtt{floor0\texttt{\_}amplitude\texttt{\_}bits}}-1)\sqrt{p+q}}
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- \mathtt{floor0\texttt{\_}amplitude\texttt{\_}offset} \right) \right)
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\end{displaymath}
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\item \varname{[iteration\_condition]} = map element \varname{[i]}
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\item \varname{[output]} element \varname{[i]} = \varname{[linear\_floor\_value]}
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\item increment \varname{[i]}
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\item if ( map element \varname{[i]} is equal to \varname{[iteration\_condition]} ) continue at step 5
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\item if ( \varname{[i]} is less than \varname{[n]} ) continue at step 2
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\item done
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\end{enumerate}
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