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diff --git a/vorbis/doc/06-floor0.tex b/vorbis/doc/06-floor0.tex deleted file mode 100644 index f3042a6..0000000 --- a/vorbis/doc/06-floor0.tex +++ /dev/null @@ -1,201 +0,0 @@ -% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*- -%!TEX root = Vorbis_I_spec.tex -\section{Floor type 0 setup and decode} \label{vorbis:spec:floor0} - -\subsection{Overview} - -Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately -known as Line Spectral Frequency or LSF) representation to encode a -smooth spectral envelope curve as the frequency response of the LSP -filter. This representation is equivalent to a traditional all-pole -infinite impulse response filter as would be used in linear predictive -coding; LSP representation may be converted to LPC representation and -vice-versa. - - - -\subsection{Floor 0 format} - -Floor zero configuration consists of six integer fields and a list of -VQ codebooks for use in coding/decoding the LSP filter coefficient -values used by each frame. - -\subsubsection{header decode} - -Configuration information for instances of floor zero decodes from the -codec setup header (third packet). configuration decode proceeds as -follows: - -\begin{Verbatim}[commandchars=\\\{\}] - 1) [floor0\_order] = read an unsigned integer of 8 bits - 2) [floor0\_rate] = read an unsigned integer of 16 bits - 3) [floor0\_bark\_map\_size] = read an unsigned integer of 16 bits - 4) [floor0\_amplitude\_bits] = read an unsigned integer of six bits - 5) [floor0\_amplitude\_offset] = read an unsigned integer of eight bits - 6) [floor0\_number\_of\_books] = read an unsigned integer of four bits and add 1 - 7) array [floor0\_book\_list] = read a list of [floor0\_number\_of\_books] unsigned integers of eight bits each; -\end{Verbatim} - -An end-of-packet condition during any of these bitstream reads renders -this stream undecodable. In addition, any element of the array -\varname{[floor0\_book\_list]} that is greater than the maximum codebook -number for this bitstream is an error condition that also renders the -stream undecodable. - - - -\subsubsection{packet decode} \label{vorbis:spec:floor0-decode} - -Extracting a floor0 curve from an audio packet consists of first -decoding the curve amplitude and \varname{[floor0\_order]} LSP -coefficient values from the bitstream, and then computing the floor -curve, which is defined as the frequency response of the decoded LSP -filter. - -Packet decode proceeds as follows: -\begin{Verbatim}[commandchars=\\\{\}] - 1) [amplitude] = read an unsigned integer of [floor0\_amplitude\_bits] bits - 2) if ( [amplitude] is greater than zero ) \{ - 3) [coefficients] is an empty, zero length vector - 4) [booknumber] = read an unsigned integer of \link{vorbis:spec:ilog}{ilog}( [floor0\_number\_of\_books] ) bits - 5) if ( [booknumber] is greater than the highest number decode codebook ) then packet is undecodable - 6) [last] = zero; - 7) vector [temp\_vector] = read vector from bitstream using codebook number [floor0\_book\_list] element [booknumber] in VQ context. - 8) add the scalar value [last] to each scalar in vector [temp\_vector] - 9) [last] = the value of the last scalar in vector [temp\_vector] - 10) concatenate [temp\_vector] onto the end of the [coefficients] vector - 11) if (length of vector [coefficients] is less than [floor0\_order], continue at step 6 - - \} - - 12) done. - -\end{Verbatim} - -Take note of the following properties of decode: -\begin{itemize} - \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. - \item An end-of-packet condition during decode should be considered a -nominal occruence; if end-of-packet is reached during any read -operation above, floor decode is to return 'unused' status as if the -\varname{[amplitude]} value had read zero at the beginning of decode. - - \item The book number used for decode -can, in fact, be stored in the bitstream in \link{vorbis:spec:ilog}{ilog}( \varname{[floor0\_number\_of\_books]} - -1 ) bits. Nevertheless, the above specification is correct and values -greater than the maximum possible book value are reserved. - - \item The number of scalars read into the vector \varname{[coefficients]} -may be greater than \varname{[floor0\_order]}, the number actually -required for curve computation. For example, if the VQ codebook used -for the floor currently being decoded has a -\varname{[codebook\_dimensions]} value of three and -\varname{[floor0\_order]} is ten, the only way to fill all the needed -scalars in \varname{[coefficients]} is to to read a total of twelve -scalars as four vectors of three scalars each. This is not an error -condition, and care must be taken not to allow a buffer overflow in -decode. The extra values are not used and may be ignored or discarded. -\end{itemize} - - - - -\subsubsection{curve computation} \label{vorbis:spec:floor0-synth} - -Given an \varname{[amplitude]} integer and \varname{[coefficients]} -vector from packet decode as well as the [floor0\_order], -[floor0\_rate], [floor0\_bark\_map\_size], [floor0\_amplitude\_bits] and -[floor0\_amplitude\_offset] values from floor setup, and an output -vector size \varname{[n]} specified by the decode process, we compute a -floor output vector. - -If the value \varname{[amplitude]} is zero, the return value is a -length \varname{[n]} vector with all-zero scalars. Otherwise, begin by -assuming the following definitions for the given vector to be -synthesized: - - \begin{displaymath} - \mathrm{map}_i = \left\{ - \begin{array}{ll} - \min ( - \mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size} - 1, - foobar - ) & \textrm{for } i \in [0,n-1] \\ - -1 & \textrm{for } i = n - \end{array} - \right. - \end{displaymath} - - where - - \begin{displaymath} - foobar = - \left\lfloor - \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})} - \right\rfloor - \end{displaymath} - - and - - \begin{displaymath} - \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2) + .0001x - \end{displaymath} - -The above is used to synthesize the LSP curve on a Bark-scale frequency -axis, then map the result to a linear-scale frequency axis. -Similarly, the below calculation synthesizes the output LSP curve \varname{[output]} on a log -(dB) amplitude scale, mapping it to linear amplitude in the last step: - -\begin{enumerate} - \item \varname{[i]} = 0 - \item \varname{[$\omega$]} = $\pi$ * map element \varname{[i]} / \varname{[floor0\_bark\_map\_size]} - \item if ( \varname{[floor0\_order]} is odd ) { - \begin{enumerate} - \item calculate \varname{[p]} and \varname{[q]} according to: - \begin{eqnarray*} - p & = & (1 - \cos^2\omega)\prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-3}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\ - q & = & \frac{1}{4} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-1}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2 - \end{eqnarray*} - - \end{enumerate} - } else \varname{[floor0\_order]} is even { - \begin{enumerate}[resume] - \item calculate \varname{[p]} and \varname{[q]} according to: - \begin{eqnarray*} - 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 \\ - q & = & \frac{(1 + \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2 - \end{eqnarray*} - - \end{enumerate} - } - - \item calculate \varname{[linear\_floor\_value]} according to: - \begin{displaymath} - \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}} - - \mathtt{floor0\texttt{\_}amplitude\texttt{\_}offset} \right) \right) - \end{displaymath} - - \item \varname{[iteration\_condition]} = map element \varname{[i]} - \item \varname{[output]} element \varname{[i]} = \varname{[linear\_floor\_value]} - \item increment \varname{[i]} - \item if ( map element \varname{[i]} is equal to \varname{[iteration\_condition]} ) continue at step 5 - \item if ( \varname{[i]} is less than \varname{[n]} ) continue at step 2 - \item done -\end{enumerate} - -\paragraph{Errata 20150227: Bark scale computation} - -Due to a typo when typesetting this version of the specification from the original HTML document, the Bark scale computation previously erroneously read: - - \begin{displaymath} - \hbox{\sout{$ - \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2 + .0001x) - $}} - \end{displaymath} - -Note that the last parenthesis is misplaced. This document now uses the correct equation as it appeared in the original HTML spec document: - - \begin{displaymath} - \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2) + .0001x - \end{displaymath} - |