| % -*- 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} |
| |
| 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\_bark\_map\_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\_rate} \cdot i}{2n}\right) \cdot \frac{\mathtt{floor0\_bark\_map\_size}} {\mathrm{bark}(.5 \cdot \mathtt{floor0\_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\_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 |
| \end{eqnarray*} |
| |
| \end{enumerate} |
| } else \varname{[floor0_order]} is even { |
| \begin{enumerate} |
| \item calculate \varname{[p]} and \varname{[q]} according to: |
| \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 |
| \end{eqnarray*} |
| |
| \end{enumerate} |
| } |
| |
| \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) |
| \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} |
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