cannam@86: % -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*- cannam@86: %!TEX root = Vorbis_I_spec.tex cannam@86: % $Id$ cannam@86: \section{Floor type 0 setup and decode} \label{vorbis:spec:floor0} cannam@86: cannam@86: \subsection{Overview} cannam@86: cannam@86: Vorbis floor type zero uses Line Spectral Pair (LSP, also alternately cannam@86: known as Line Spectral Frequency or LSF) representation to encode a cannam@86: smooth spectral envelope curve as the frequency response of the LSP cannam@86: filter. This representation is equivalent to a traditional all-pole cannam@86: infinite impulse response filter as would be used in linear predictive cannam@86: coding; LSP representation may be converted to LPC representation and cannam@86: vice-versa. cannam@86: cannam@86: cannam@86: cannam@86: \subsection{Floor 0 format} cannam@86: cannam@86: Floor zero configuration consists of six integer fields and a list of cannam@86: VQ codebooks for use in coding/decoding the LSP filter coefficient cannam@86: values used by each frame. cannam@86: cannam@86: \subsubsection{header decode} cannam@86: cannam@86: Configuration information for instances of floor zero decodes from the cannam@86: codec setup header (third packet). configuration decode proceeds as cannam@86: follows: cannam@86: cannam@86: \begin{Verbatim}[commandchars=\\\{\}] cannam@86: 1) [floor0\_order] = read an unsigned integer of 8 bits cannam@86: 2) [floor0\_rate] = read an unsigned integer of 16 bits cannam@86: 3) [floor0\_bark\_map\_size] = read an unsigned integer of 16 bits cannam@86: 4) [floor0\_amplitude\_bits] = read an unsigned integer of six bits cannam@86: 5) [floor0\_amplitude\_offset] = read an unsigned integer of eight bits cannam@86: 6) [floor0\_number\_of\_books] = read an unsigned integer of four bits and add 1 cannam@86: 7) array [floor0\_book\_list] = read a list of [floor0\_number\_of\_books] unsigned integers of eight bits each; cannam@86: \end{Verbatim} cannam@86: cannam@86: An end-of-packet condition during any of these bitstream reads renders cannam@86: this stream undecodable. In addition, any element of the array cannam@86: \varname{[floor0\_book\_list]} that is greater than the maximum codebook cannam@86: number for this bitstream is an error condition that also renders the cannam@86: stream undecodable. cannam@86: cannam@86: cannam@86: cannam@86: \subsubsection{packet decode} \label{vorbis:spec:floor0-decode} cannam@86: cannam@86: Extracting a floor0 curve from an audio packet consists of first cannam@86: decoding the curve amplitude and \varname{[floor0\_order]} LSP cannam@86: coefficient values from the bitstream, and then computing the floor cannam@86: curve, which is defined as the frequency response of the decoded LSP cannam@86: filter. cannam@86: cannam@86: Packet decode proceeds as follows: cannam@86: \begin{Verbatim}[commandchars=\\\{\}] cannam@86: 1) [amplitude] = read an unsigned integer of [floor0\_amplitude\_bits] bits cannam@86: 2) if ( [amplitude] is greater than zero ) \{ cannam@86: 3) [coefficients] is an empty, zero length vector cannam@86: 4) [booknumber] = read an unsigned integer of \link{vorbis:spec:ilog}{ilog}( [floor0\_number\_of\_books] ) bits cannam@86: 5) if ( [booknumber] is greater than the highest number decode codebook ) then packet is undecodable cannam@86: 6) [last] = zero; cannam@86: 7) vector [temp\_vector] = read vector from bitstream using codebook number [floor0\_book\_list] element [booknumber] in VQ context. cannam@86: 8) add the scalar value [last] to each scalar in vector [temp\_vector] cannam@86: 9) [last] = the value of the last scalar in vector [temp\_vector] cannam@86: 10) concatenate [temp\_vector] onto the end of the [coefficients] vector cannam@86: 11) if (length of vector [coefficients] is less than [floor0\_order], continue at step 6 cannam@86: cannam@86: \} cannam@86: cannam@86: 12) done. cannam@86: cannam@86: \end{Verbatim} cannam@86: cannam@86: Take note of the following properties of decode: cannam@86: \begin{itemize} cannam@86: \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. cannam@86: \item An end-of-packet condition during decode should be considered a cannam@86: nominal occruence; if end-of-packet is reached during any read cannam@86: operation above, floor decode is to return 'unused' status as if the cannam@86: \varname{[amplitude]} value had read zero at the beginning of decode. cannam@86: cannam@86: \item The book number used for decode cannam@86: can, in fact, be stored in the bitstream in \link{vorbis:spec:ilog}{ilog}( \varname{[floor0\_number\_of\_books]} - cannam@86: 1 ) bits. Nevertheless, the above specification is correct and values cannam@86: greater than the maximum possible book value are reserved. cannam@86: cannam@86: \item The number of scalars read into the vector \varname{[coefficients]} cannam@86: may be greater than \varname{[floor0\_order]}, the number actually cannam@86: required for curve computation. For example, if the VQ codebook used cannam@86: for the floor currently being decoded has a cannam@86: \varname{[codebook\_dimensions]} value of three and cannam@86: \varname{[floor0\_order]} is ten, the only way to fill all the needed cannam@86: scalars in \varname{[coefficients]} is to to read a total of twelve cannam@86: scalars as four vectors of three scalars each. This is not an error cannam@86: condition, and care must be taken not to allow a buffer overflow in cannam@86: decode. The extra values are not used and may be ignored or discarded. cannam@86: \end{itemize} cannam@86: cannam@86: cannam@86: cannam@86: cannam@86: \subsubsection{curve computation} \label{vorbis:spec:floor0-synth} cannam@86: cannam@86: Given an \varname{[amplitude]} integer and \varname{[coefficients]} cannam@86: vector from packet decode as well as the [floor0\_order], cannam@86: [floor0\_rate], [floor0\_bark\_map\_size], [floor0\_amplitude\_bits] and cannam@86: [floor0\_amplitude\_offset] values from floor setup, and an output cannam@86: vector size \varname{[n]} specified by the decode process, we compute a cannam@86: floor output vector. cannam@86: cannam@86: If the value \varname{[amplitude]} is zero, the return value is a cannam@86: length \varname{[n]} vector with all-zero scalars. Otherwise, begin by cannam@86: assuming the following definitions for the given vector to be cannam@86: synthesized: cannam@86: cannam@86: \begin{displaymath} cannam@86: \mathrm{map}_i = \left\{ cannam@86: \begin{array}{ll} cannam@86: \min ( cannam@86: \mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size} - 1, cannam@86: foobar cannam@86: ) & \textrm{for } i \in [0,n-1] \\ cannam@86: -1 & \textrm{for } i = n cannam@86: \end{array} cannam@86: \right. cannam@86: \end{displaymath} cannam@86: cannam@86: where cannam@86: cannam@86: \begin{displaymath} cannam@86: foobar = cannam@86: \left\lfloor cannam@86: \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})} cannam@86: \right\rfloor cannam@86: \end{displaymath} cannam@86: cannam@86: and cannam@86: cannam@86: \begin{displaymath} cannam@86: \mathrm{bark}(x) = 13.1 \arctan (.00074x) + 2.24 \arctan (.0000000185x^2 + .0001x) cannam@86: \end{displaymath} cannam@86: cannam@86: The above is used to synthesize the LSP curve on a Bark-scale frequency cannam@86: axis, then map the result to a linear-scale frequency axis. cannam@86: Similarly, the below calculation synthesizes the output LSP curve \varname{[output]} on a log cannam@86: (dB) amplitude scale, mapping it to linear amplitude in the last step: cannam@86: cannam@86: \begin{enumerate} cannam@86: \item \varname{[i]} = 0 cannam@86: \item \varname{[$\omega$]} = $\pi$ * map element \varname{[i]} / \varname{[floor0\_bark\_map\_size]} cannam@86: \item if ( \varname{[floor0\_order]} is odd ) { cannam@86: \begin{enumerate} cannam@86: \item calculate \varname{[p]} and \varname{[q]} according to: cannam@86: \begin{eqnarray*} cannam@86: p & = & (1 - \cos^2\omega)\prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-3}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\ cannam@86: q & = & \frac{1}{4} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-1}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2 cannam@86: \end{eqnarray*} cannam@86: cannam@86: \end{enumerate} cannam@86: } else \varname{[floor0\_order]} is even { cannam@86: \begin{enumerate}[resume] cannam@86: \item calculate \varname{[p]} and \varname{[q]} according to: cannam@86: \begin{eqnarray*} cannam@86: 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 \\ cannam@86: q & = & \frac{(1 + \cos\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\texttt{\_}order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2 cannam@86: \end{eqnarray*} cannam@86: cannam@86: \end{enumerate} cannam@86: } cannam@86: cannam@86: \item calculate \varname{[linear\_floor\_value]} according to: cannam@86: \begin{displaymath} cannam@86: \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}} cannam@86: - \mathtt{floor0\texttt{\_}amplitude\texttt{\_}offset} \right) \right) cannam@86: \end{displaymath} cannam@86: cannam@86: \item \varname{[iteration\_condition]} = map element \varname{[i]} cannam@86: \item \varname{[output]} element \varname{[i]} = \varname{[linear\_floor\_value]} cannam@86: \item increment \varname{[i]} cannam@86: \item if ( map element \varname{[i]} is equal to \varname{[iteration\_condition]} ) continue at step 5 cannam@86: \item if ( \varname{[i]} is less than \varname{[n]} ) continue at step 2 cannam@86: \item done cannam@86: \end{enumerate} cannam@86: cannam@86: cannam@86: cannam@86: cannam@86: cannam@86: cannam@86: