mirror of
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a745fc3757
added libraries: opus flac libsndfile updated: libvorbis libogg openal - Everything works as expected for now. Bare in mind libsndfile needed the check for whether or not it could find the xiph libraries removed in order for this to work.
201 lines
8.9 KiB
TeX
201 lines
8.9 KiB
TeX
% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-
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%!TEX root = Vorbis_I_spec.tex
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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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\paragraph{Errata 20150227: Bark scale computation}
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Due to a typo when typesetting this version of the specification from the original HTML document, the Bark scale computation previously erroneously read:
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\begin{displaymath}
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\hbox{\sout{$
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\mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2 + .0001x)
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$}}
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\end{displaymath}
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Note that the last parenthesis is misplaced. This document now uses the correct equation as it appeared in the original HTML spec document:
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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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