% -*- mode: latex; TeX-master: "Vorbis_I_spec"; -*-
%!TEX root = Vorbis_I_spec.tex
-% $Id$
\section{Floor type 0 setup and decode} \label{vorbis:spec:floor0}
\subsection{Overview}
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;
+ 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
+\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
+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
+ 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
+ 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
+ 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
\}
\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]} -
+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
+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
+\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
\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 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.
\mathrm{map}_i = \left\{
\begin{array}{ll}
\min (
- \mathtt{floor0\_bark\_map\_size} - 1,
+ \mathtt{floor0\texttt{\_}bark\texttt{\_}map\texttt{\_}size} - 1,
foobar
) & \textrm{for } i \in [0,n-1] \\
-1 & \textrm{for } i = n
\begin{displaymath}
foobar =
\left\lfloor
- \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})}
+ \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)
+ \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
\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 ) {
+ \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:
-\TODO{the following is generated from the TeX code embedded into the DocBook files:}
- \begin{eqnarray*}
- p & = & (1 - \cos^2\omega)\prod_{j=0}^{(\mathtt{order}-3)/2} 4 (\cos c_{2j+1} - \cos \omega)^2 \\
- q & = & \frac{1}{4} \prod_{j=0}^{(\mathtt{order}-1)/2} 4 (\cos c_{2j+1} - \cos \omega)^2
- \end{eqnarray*}
-
-\TODO{the following is what oddlsp.png contains:}
\begin{eqnarray*}
- p & = & (1 - \cos^2\omega)\prod_{j=0}^{\frac{\mathtt{floor0\_order}-3}{2}} 4 (\cos([\mathtt{coefficients}]_{2j+1}) - \cos \omega)^2 \\
- q & = & \frac{1}{4} \prod_{j=0}^{\frac{\mathtt{floor0\_order}-1}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
+ 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}
+ } else \varname{[floor0\_order]} is even {
+ \begin{enumerate}[resume]
\item calculate \varname{[p]} and \varname{[q]} according to:
-\TODO{the following is generated from the TeX code embedded into the DocBook files:}
- \begin{eqnarray*}
- p & = & \frac{(1 - \cos^2\omega)}{2} \prod_{j=0}^{(\mathtt{order}-2)/2} 4 (\cos c_{2j} - \cos \omega)^2 \\
- q & = & \frac{(1 + \cos^2\omega)}{2} \prod_{j=0}^{(\mathtt{order}-2)/2} 4 (\cos c_{2j} - \cos \omega)^2
- \end{eqnarray*}
-
-\TODO{the following is what oddlsp.png contains:}
\begin{eqnarray*}
- 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 \\
- q & = & \frac{(1 + \cos^2\omega)}{2} \prod_{j=0}^{\frac{\mathtt{floor0\_order}-2}{2}} 4 (\cos([\mathtt{coefficients}]_{2j}) - \cos \omega)^2
+ 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:
+ \item calculate \varname{[linear\_floor\_value]} according to:
\begin{displaymath}
- \exp \left( .11512925 \left(\frac{\mathtt{amplitude} \cdot \mathtt{floor0\_amplitute\_offset}}{(2^{\mathtt{floor0\_amplitude\_bits}}-1)\sqrt{p+q}}
- - \mathtt{floor0\_amplitude\_offset} \right) \right)
+ \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 \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 ( 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}
projects / platform / upstream / libvorbis.git / blobdiff