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\section{Codec Setup and Packet Decode} \label{vorbis:spec:codec}

\subsection{Overview}

This document serves as the top-level reference document for the

bit-by-bit decode specification of Vorbis I.  This document assumes a

high-level understanding of the Vorbis decode process, which is

provided in \xref{vorbis:spec:intro}.  \xref{vorbis:spec:bitpacking} covers reading and writing bit fields from

and to bitstream packets.

\subsection{Header decode and decode setup}

A Vorbis bitstream begins with three header packets. The header

packets are, in order, the identification header, the comments header,

and the setup header. All are required for decode compliance.  An

end-of-packet condition during decoding the first or third header

packet renders the stream undecodable.  End-of-packet decoding the

comment header is a non-fatal error condition.

\subsubsection{Common header decode}

Each header packet begins with the same header fields.

\begin{Verbatim}[commandchars=\\\{\}]

  1) [packet\_type] : 8 bit value

  2) 0x76, 0x6f, 0x72, 0x62, 0x69, 0x73: the characters 'v','o','r','b','i','s' as six octets

\end{Verbatim}

Decode continues according to packet type; the identification header

is type 1, the comment header type 3 and the setup header type 5

(these types are all odd as a packet with a leading single bit of '0'

is an audio packet).  The packets must occur in the order of

identification, comment, setup.

\subsubsection{Identification header}

The identification header is a short header of only a few fields used

to declare the stream definitively as Vorbis, and provide a few externally

relevant pieces of information about the audio stream. The

identification header is coded as follows:

\begin{Verbatim}[commandchars=\\\{\}]

 1) [vorbis\_version] = read 32 bits as unsigned integer

 2) [audio\_channels] = read 8 bit integer as unsigned

 3) [audio\_sample\_rate] = read 32 bits as unsigned integer

 4) [bitrate\_maximum] = read 32 bits as signed integer

 5) [bitrate\_nominal] = read 32 bits as signed integer

 6) [bitrate\_minimum] = read 32 bits as signed integer

 7) [blocksize\_0] = 2 exponent (read 4 bits as unsigned integer)

 8) [blocksize\_1] = 2 exponent (read 4 bits as unsigned integer)

 9) [framing\_flag] = read one bit

\end{Verbatim}

\varname{[vorbis\_version]} is to read '0' in order to be compatible

with this document.  Both \varname{[audio\_channels]} and

\varname{[audio\_sample\_rate]} must read greater than zero.  Allowed final

blocksize values are 64, 128, 256, 512, 1024, 2048, 4096 and 8192 in

Vorbis I.  \varname{[blocksize\_0]} must be less than or equal to

\varname{[blocksize\_1]}.  The framing bit must be nonzero.  Failure to

meet any of these conditions renders a stream undecodable.

The bitrate fields above are used only as hints. The nominal bitrate

field especially may be considerably off in purely VBR streams.  The

fields are meaningful only when greater than zero.

\begin{itemize}

  \item All three fields set to the same value implies a fixed rate, or tightly bounded, nearly fixed-rate bitstream

  \item Only nominal set implies a VBR or ABR stream that averages the nominal bitrate

  \item Maximum and or minimum set implies a VBR bitstream that obeys the bitrate limits

  \item None set indicates the encoder does not care to speculate.

\end{itemize}

\subsubsection{Comment header}

Comment header decode and data specification is covered in

\xref{vorbis:spec:comment}.

\subsubsection{Setup header}

Vorbis codec setup is configurable to an extreme degree:

\begin{center}

\includegraphics[width=\textwidth]{components}

\captionof{figure}{decoder pipeline configuration}

\end{center}

The setup header contains the bulk of the codec setup information

needed for decode.  The setup header contains, in order, the lists of

codebook configurations, time-domain transform configurations

(placeholders in Vorbis I), floor configurations, residue

configurations, channel mapping configurations and mode

configurations. It finishes with a framing bit of '1'.  Header decode

proceeds in the following order:

\paragraph{Codebooks}

\begin{enumerate}

\item \varname{[vorbis\_codebook\_count]} = read eight bits as unsigned integer and add one

\item Decode \varname{[vorbis\_codebook\_count]} codebooks in order as defined

in \xref{vorbis:spec:codebook}.  Save each configuration, in

order, in an array of

codebook configurations \varname{[vorbis\_codebook\_configurations]}.

\end{enumerate}

\paragraph{Time domain transforms}

These hooks are placeholders in Vorbis I.  Nevertheless, the

configuration placeholder values must be read to maintain bitstream

sync.

\begin{enumerate}

\item \varname{[vorbis\_time\_count]} = read 6 bits as unsigned integer and add one

\item read \varname{[vorbis\_time\_count]} 16 bit values; each value should be zero.  If any value is nonzero, this is an error condition and the stream is undecodable.

\end{enumerate}

\paragraph{Floors}

Vorbis uses two floor types; header decode is handed to the decode

abstraction of the appropriate type.

\begin{enumerate}

 \item \varname{[vorbis\_floor\_count]} = read 6 bits as unsigned integer and add one

 \item For each \varname{[i]} of \varname{[vorbis\_floor\_count]} floor numbers:

  \begin{enumerate}

   \item read the floor type: vector \varname{[vorbis\_floor\_types]} element \varname{[i]} =

read 16 bits as unsigned integer

   \item If the floor type is zero, decode the floor

configuration as defined in \xref{vorbis:spec:floor0}; save

this

configuration in slot \varname{[i]} of the floor configuration array \varname{[vorbis\_floor\_configurations]}.

   \item If the floor type is one,

decode the floor configuration as defined in \xref{vorbis:spec:floor1}; save this configuration in slot \varname{[i]} of the floor configuration array \varname{[vorbis\_floor\_configurations]}.

   \item If the the floor type is greater than one, this stream is undecodable; ERROR CONDITION

  \end{enumerate}

\end{enumerate}

\paragraph{Residues}

Vorbis uses three residue types; header decode of each type is identical.

\begin{enumerate}

\item \varname{[vorbis\_residue\_count]} = read 6 bits as unsigned integer and add one

\item For each of \varname{[vorbis\_residue\_count]} residue numbers:

 \begin{enumerate}

  \item read the residue type; vector \varname{[vorbis\_residue\_types]} element \varname{[i]} = read 16 bits as unsigned integer

  \item If the residue type is zero,

one or two, decode the residue configuration as defined in \xref{vorbis:spec:residue}; save this configuration in slot \varname{[i]} of the residue configuration array \varname{[vorbis\_residue\_configurations]}.

  \item If the the residue type is greater than two, this stream is undecodable; ERROR CONDITION

 \end{enumerate}

\end{enumerate}

\paragraph{Mappings}

Mappings are used to set up specific pipelines for encoding

multichannel audio with varying channel mapping applications. Vorbis I

uses a single mapping type (0), with implicit PCM channel mappings.

% FIXME/TODO: LaTeX cannot nest enumerate that deeply, so I have to use

% itemize at the innermost level. However, it would be much better to 

% rewrite this pseudocode using listings or algoritmicx or some other

% package geared towards this.

\begin{enumerate}

 \item \varname{[vorbis\_mapping\_count]} = read 6 bits as unsigned integer and add one

 \item For each \varname{[i]} of \varname{[vorbis\_mapping\_count]} mapping numbers:

  \begin{enumerate}

   \item read the mapping type: 16 bits as unsigned integer.  There's no reason to save the mapping type in Vorbis I.

   \item If the mapping type is nonzero, the stream is undecodable

   \item If the mapping type is zero:

    \begin{enumerate}

     \item read 1 bit as a boolean flag

      \begin{enumerate}

       \item if set, \varname{[vorbis\_mapping\_submaps]} = read 4 bits as unsigned integer and add one

       \item if unset, \varname{[vorbis\_mapping\_submaps]} = 1

      \end{enumerate}

     \item read 1 bit as a boolean flag

       \begin{enumerate}

         \item if set, square polar channel mapping is in use:

           \begin{itemize}

             \item \varname{[vorbis\_mapping\_coupling\_steps]} = read 8 bits as unsigned integer and add one

             \item for \varname{[j]} each of \varname{[vorbis\_mapping\_coupling\_steps]} steps:

               \begin{itemize}

                 \item vector \varname{[vorbis\_mapping\_magnitude]} element \varname{[j]}= read \link{vorbis:spec:ilog}{ilog}(\varname{[audio\_channels]} - 1) bits as unsigned integer

                 \item vector \varname{[vorbis\_mapping\_angle]} element \varname{[j]}= read \link{vorbis:spec:ilog}{ilog}(\varname{[audio\_channels]} - 1) bits as unsigned integer

                 \item the numbers read in the above two steps are channel numbers representing the channel to treat as magnitude and the channel to treat as angle, respectively.  If for any coupling step the angle channel number equals the magnitude channel number, the magnitude channel number is greater than \varname{[audio\_channels]}-1, or the angle channel is greater than \varname{[audio\_channels]}-1, the stream is undecodable.

               \end{itemize}

           \end{itemize}

         \item if unset, \varname{[vorbis\_mapping\_coupling\_steps]} = 0

       \end{enumerate}

     \item read 2 bits (reserved field); if the value is nonzero, the stream is undecodable

     \item if \varname{[vorbis\_mapping\_submaps]} is greater than one, we read channel multiplex settings. For each \varname{[j]} of \varname{[audio\_channels]} channels:

      \begin{enumerate}

       \item vector \varname{[vorbis\_mapping\_mux]} element \varname{[j]} = read 4 bits as unsigned integer

       \item if the value is greater than the highest numbered submap (\varname{[vorbis\_mapping\_submaps]} - 1), this in an error condition rendering the stream undecodable

      \end{enumerate}

     \item for each submap \varname{[j]} of \varname{[vorbis\_mapping\_submaps]} submaps, read the floor and residue numbers for use in decoding that submap:

      \begin{enumerate}

       \item read and discard 8 bits (the unused time configuration placeholder)

       \item read 8 bits as unsigned integer for the floor number; save in vector \varname{[vorbis\_mapping\_submap\_floor]} element \varname{[j]}

       \item verify the floor number is not greater than the highest number floor configured for the bitstream. If it is, the bitstream is undecodable

       \item read 8 bits as unsigned integer for the residue number; save in vector \varname{[vorbis\_mapping\_submap\_residue]} element \varname{[j]}

       \item verify the residue number is not greater than the highest number residue configured for the bitstream.  If it is, the bitstream is undecodable

      \end{enumerate}

     \item save this mapping configuration in slot \varname{[i]} of the mapping configuration array \varname{[vorbis\_mapping\_configurations]}.

    \end{enumerate}

  \end{enumerate}

\end{enumerate}

\paragraph{Modes}

\begin{enumerate}

 \item \varname{[vorbis\_mode\_count]} = read 6 bits as unsigned integer and add one

 \item For each of \varname{[vorbis\_mode\_count]} mode numbers:

  \begin{enumerate}

  \item \varname{[vorbis\_mode\_blockflag]} = read 1 bit

  \item \varname{[vorbis\_mode\_windowtype]} = read 16 bits as unsigned integer

  \item \varname{[vorbis\_mode\_transformtype]} = read 16 bits as unsigned integer

  \item \varname{[vorbis\_mode\_mapping]} = read 8 bits as unsigned integer

  \item verify ranges; zero is the only legal value in Vorbis I for

\varname{[vorbis\_mode\_windowtype]}

and \varname{[vorbis\_mode\_transformtype]}.  \varname{[vorbis\_mode\_mapping]} must not be greater than the highest number mapping in use.  Any illegal values render the stream undecodable.

  \item save this mode configuration in slot \varname{[i]} of the mode configuration array

\varname{[vorbis\_mode\_configurations]}.

 \end{enumerate}

\item read 1 bit as a framing flag.  If unset, a framing error occurred and the stream is not

decodable.

\end{enumerate}

After reading mode descriptions, setup header decode is complete.

\subsection{Audio packet decode and synthesis}

Following the three header packets, all packets in a Vorbis I stream

are audio.  The first step of audio packet decode is to read and

verify the packet type. \emph{A non-audio packet when audio is expected

indicates stream corruption or a non-compliant stream. The decoder

must ignore the packet and not attempt decoding it to audio}.

\subsubsection{packet type, mode and window decode}

\begin{enumerate}

 \item read 1 bit \varname{[packet\_type]}; check that packet type is 0 (audio)

 \item read \link{vorbis:spec:ilog}{ilog}([vorbis\_mode\_count]-1) bits

\varname{[mode\_number]}

 \item decode blocksize \varname{[n]} is equal to \varname{[blocksize\_0]} if

\varname{[vorbis\_mode\_blockflag]} is 0, else \varname{[n]} is equal to \varname{[blocksize\_1]}.

 \item perform window selection and setup; this window is used later by the inverse MDCT:

  \begin{enumerate}

   \item if this is a long window (the \varname{[vorbis\_mode\_blockflag]} flag of this mode is

set):

    \begin{enumerate}

     \item read 1 bit for \varname{[previous\_window\_flag]}

     \item read 1 bit for \varname{[next\_window\_flag]}

     \item if \varname{[previous\_window\_flag]} is not set, the left half

         of the window will be a hybrid window for lapping with a

         short block.  See \xref{vorbis:spec:window} for an illustration of overlapping

dissimilar

         windows. Else, the left half window will have normal long

         shape.

     \item if \varname{[next\_window\_flag]} is not set, the right half of

         the window will be a hybrid window for lapping with a short

         block.  See \xref{vorbis:spec:window} for an

illustration of overlapping dissimilar

         windows. Else, the left right window will have normal long

         shape.

    \end{enumerate}

   \item  if this is a short window, the window is always the same

       short-window shape.

  \end{enumerate}

\end{enumerate}

Vorbis windows all use the slope function $y=\sin(\frac{\pi}{2} * \sin^2((x+0.5)/n * \pi))$,

where $n$ is window size and $x$ ranges $0 \ldots n-1$, but dissimilar

lapping requirements can affect overall shape.  Window generation

proceeds as follows:

\begin{enumerate}

 \item  \varname{[window\_center]} = \varname{[n]} / 2

 \item  if (\varname{[vorbis\_mode\_blockflag]} is set and \varname{[previous\_window\_flag]} is

not set) then

  \begin{enumerate}

   \item \varname{[left\_window\_start]} = \varname{[n]}/4 -

\varname{[blocksize\_0]}/4

   \item \varname{[left\_window\_end]} = \varname{[n]}/4 + \varname{[blocksize\_0]}/4

   \item \varname{[left\_n]} = \varname{[blocksize\_0]}/2

  \end{enumerate}

 else

  \begin{enumerate}

   \item \varname{[left\_window\_start]} = 0

   \item \varname{[left\_window\_end]} = \varname{[window\_center]}

   \item \varname{[left\_n]} = \varname{[n]}/2

  \end{enumerate}

 \item  if (\varname{[vorbis\_mode\_blockflag]} is set and \varname{[next\_window\_flag]} is not

set) then

  \begin{enumerate}

   \item \varname{[right\_window\_start]} = \varname{[n]*3}/4 -

\varname{[blocksize\_0]}/4

   \item \varname{[right\_window\_end]} = \varname{[n]*3}/4 +

\varname{[blocksize\_0]}/4

   \item \varname{[right\_n]} = \varname{[blocksize\_0]}/2

  \end{enumerate}

 else

  \begin{enumerate}

   \item \varname{[right\_window\_start]} = \varname{[window\_center]}

   \item \varname{[right\_window\_end]} = \varname{[n]}

   \item \varname{[right\_n]} = \varname{[n]}/2

  \end{enumerate}

 \item  window from range 0 ... \varname{[left\_window\_start]}-1 inclusive is zero

 \item  for \varname{[i]} in range \varname{[left\_window\_start]} ...

\varname{[left\_window\_end]}-1, window(\varname{[i]}) = $\sin(\frac{\pi}{2} * \sin^2($ (\varname{[i]}-\varname{[left\_window\_start]}+0.5) / \varname{[left\_n]} $* \frac{\pi}{2})$ )

 \item  window from range \varname{[left\_window\_end]} ... \varname{[right\_window\_start]}-1

inclusive is one\item  for \varname{[i]} in range \varname{[right\_window\_start]} ... \varname{[right\_window\_end]}-1, window(\varname{[i]}) = $\sin(\frac{\pi}{2} * \sin^2($ (\varname{[i]}-\varname{[right\_window\_start]}+0.5) / \varname{[right\_n]} $ * \frac{\pi}{2} + \frac{\pi}{2})$ )

\item  window from range \varname{[right\_window\_start]} ... \varname{[n]}-1 is

zero

\end{enumerate}

An end-of-packet condition up to this point should be considered an

error that discards this packet from the stream.  An end of packet

condition past this point is to be considered a possible nominal

occurrence.

\subsubsection{floor curve decode}

From this point on, we assume out decode context is using mode number

\varname{[mode\_number]} from configuration array

\varname{[vorbis\_mode\_configurations]} and the map number

\varname{[vorbis\_mode\_mapping]} (specified by the current mode) taken

from the mapping configuration array

\varname{[vorbis\_mapping\_configurations]}.

Floor curves are decoded one-by-one in channel order.

For each floor \varname{[i]} of \varname{[audio\_channels]}

 \begin{enumerate}

  \item \varname{[submap\_number]} = element \varname{[i]} of vector [vorbis\_mapping\_mux]

  \item \varname{[floor\_number]} = element \varname{[submap\_number]} of vector

[vorbis\_submap\_floor]

  \item if the floor type of this

floor (vector \varname{[vorbis\_floor\_types]} element

\varname{[floor\_number]}) is zero then decode the floor for

channel \varname{[i]} according to the

\xref{vorbis:spec:floor0-decode}

  \item if the type of this floor

is one then decode the floor for channel \varname{[i]} according

to the \xref{vorbis:spec:floor1-decode}

  \item save the needed decoded floor information for channel for later synthesis

  \item if the decoded floor returned 'unused', set vector \varname{[no\_residue]} element

\varname{[i]} to true, else set vector \varname{[no\_residue]} element \varname{[i]} to

false

 \end{enumerate}

An end-of-packet condition during floor decode shall result in packet

decode zeroing all channel output vectors and skipping to the

add/overlap output stage.

\subsubsection{nonzero vector propagate}

A possible result of floor decode is that a specific vector is marked

'unused' which indicates that that final output vector is all-zero

values (and the floor is zero).  The residue for that vector is not

coded in the stream, save for one complication.  If some vectors are

used and some are not, channel coupling could result in mixing a

zeroed and nonzeroed vector to produce two nonzeroed vectors.

for each \varname{[i]} from 0 ... \varname{[vorbis\_mapping\_coupling\_steps]}-1

\begin{enumerate}

 \item if either \varname{[no\_residue]} entry for channel

(\varname{[vorbis\_mapping\_magnitude]} element \varname{[i]})

or channel

(\varname{[vorbis\_mapping\_angle]} element \varname{[i]})

are set to false, then both must be set to false.  Note that an 'unused'

floor has no decoded floor information; it is important that this is

remembered at floor curve synthesis time.

\end{enumerate}

\subsubsection{residue decode}

Unlike floors, which are decoded in channel order, the residue vectors

are decoded in submap order.

for each submap \varname{[i]} in order from 0 ... \varname{[vorbis\_mapping\_submaps]}-1

\begin{enumerate}

 \item \varname{[ch]} = 0

 \item for each channel \varname{[j]} in order from 0 ... \varname{[audio\_channels]} - 1

  \begin{enumerate}

   \item if channel \varname{[j]} in submap \varname{[i]} (vector \varname{[vorbis\_mapping\_mux]} element \varname{[j]} is equal to \varname{[i]})

    \begin{enumerate}

     \item if vector \varname{[no\_residue]} element \varname{[j]} is true

      \begin{enumerate}

       \item vector \varname{[do\_not\_decode\_flag]} element \varname{[ch]} is set

      \end{enumerate}

     else

      \begin{enumerate}

       \item vector \varname{[do\_not\_decode\_flag]} element \varname{[ch]} is unset

      \end{enumerate}

     \item increment \varname{[ch]}

    \end{enumerate}

  \end{enumerate}

 \item \varname{[residue\_number]} = vector \varname{[vorbis\_mapping\_submap\_residue]} element \varname{[i]}

 \item \varname{[residue\_type]} = vector \varname{[vorbis\_residue\_types]} element \varname{[residue\_number]}

 \item decode \varname{[ch]} vectors using residue \varname{[residue\_number]}, according to type \varname{[residue\_type]}, also passing vector \varname{[do\_not\_decode\_flag]} to indicate which vectors in the bundle should not be decoded. Correct per-vector decode length is \varname{[n]}/2.

 \item \varname{[ch]} = 0

 \item for each channel \varname{[j]} in order from 0 ... \varname{[audio\_channels]}

  \begin{enumerate}

   \item if channel \varname{[j]} is in submap \varname{[i]} (vector \varname{[vorbis\_mapping\_mux]} element \varname{[j]} is equal to \varname{[i]})

    \begin{enumerate}

     \item residue vector for channel \varname{[j]} is set to decoded residue vector \varname{[ch]}

     \item increment \varname{[ch]}

    \end{enumerate}

  \end{enumerate}

\end{enumerate}

\subsubsection{inverse coupling}

for each \varname{[i]} from \varname{[vorbis\_mapping\_coupling\_steps]}-1 descending to 0

\begin{enumerate}

 \item \varname{[magnitude\_vector]} = the residue vector for channel

(vector \varname{[vorbis\_mapping\_magnitude]} element \varname{[i]})

 \item \varname{[angle\_vector]} = the residue vector for channel (vector

\varname{[vorbis\_mapping\_angle]} element \varname{[i]})

 \item for each scalar value \varname{[M]} in vector \varname{[magnitude\_vector]} and the corresponding scalar value \varname{[A]} in vector \varname{[angle\_vector]}:

  \begin{enumerate}

   \item if (\varname{[M]} is greater than zero)

    \begin{enumerate}

     \item if (\varname{[A]} is greater than zero)

      \begin{enumerate}

       \item \varname{[new\_M]} = \varname{[M]}

       \item \varname{[new\_A]} = \varname{[M]}-\varname{[A]}

      \end{enumerate}

     else

      \begin{enumerate}

       \item \varname{[new\_A]} = \varname{[M]}

       \item \varname{[new\_M]} = \varname{[M]}+\varname{[A]}

      \end{enumerate}

    \end{enumerate}

   else

    \begin{enumerate}

     \item if (\varname{[A]} is greater than zero)

      \begin{enumerate}

       \item \varname{[new\_M]} = \varname{[M]}

       \item \varname{[new\_A]} = \varname{[M]}+\varname{[A]}

      \end{enumerate}

     else

      \begin{enumerate}

       \item \varname{[new\_A]} = \varname{[M]}

       \item \varname{[new\_M]} = \varname{[M]}-\varname{[A]}

      \end{enumerate}

    \end{enumerate}

   \item set scalar value \varname{[M]} in vector \varname{[magnitude\_vector]} to \varname{[new\_M]}

   \item set scalar value \varname{[A]} in vector \varname{[angle\_vector]} to \varname{[new\_A]}

  \end{enumerate}

\end{enumerate}

\subsubsection{dot product}

For each channel, synthesize the floor curve from the decoded floor

information, according to packet type. Note that the vector synthesis

length for floor computation is \varname{[n]}/2.

For each channel, multiply each element of the floor curve by each

element of that channel's residue vector.  The result is the dot

product of the floor and residue vectors for each channel; the produced

vectors are the length \varname{[n]}/2 audio spectrum for each

channel.

% TODO/FIXME: The following two paragraphs have identical twins

%   in section 1 (under "compute floor/residue dot product")

One point is worth mentioning about this dot product; a common mistake

in a fixed point implementation might be to assume that a 32 bit

fixed-point representation for floor and residue and direct

multiplication of the vectors is sufficient for acceptable spectral

depth in all cases because it happens to mostly work with the current

Xiph.Org reference encoder.

However, floor vector values can span \~140dB (\~24 bits unsigned), and

the audio spectrum vector should represent a minimum of 120dB (\~21

bits with sign), even when output is to a 16 bit PCM device.  For the

residue vector to represent full scale if the floor is nailed to

$-140$dB, it must be able to span 0 to $+140$dB.  For the residue vector

to reach full scale if the floor is nailed at 0dB, it must be able to

represent $-140$dB to $+0$dB.  Thus, in order to handle full range

dynamics, a residue vector may span $-140$dB to $+140$dB entirely within

spec.  A 280dB range is approximately 48 bits with sign; thus the

residue vector must be able to represent a 48 bit range and the dot

product must be able to handle an effective 48 bit times 24 bit

multiplication.  This range may be achieved using large (64 bit or

larger) integers, or implementing a movable binary point

representation.

\subsubsection{inverse MDCT}

Convert the audio spectrum vector of each channel back into time

domain PCM audio via an inverse Modified Discrete Cosine Transform

(MDCT).  A detailed description of the MDCT is available in \cite{Sporer/Brandenburg/Edler}.  The window

function used for the MDCT is the function described earlier.

\subsubsection{overlap\_add}

Windowed MDCT output is overlapped and added with the right hand data

of the previous window such that the 3/4 point of the previous window

is aligned with the 1/4 point of the current window (as illustrated in

\xref{vorbis:spec:window}).  The overlapped portion

produced from overlapping the previous and current frame data is

finished data to be returned by the decoder.  This data spans from the

center of the previous window to the center of the current window.  In

the case of same-sized windows, the amount of data to return is

one-half block consisting of and only of the overlapped portions. When

overlapping a short and long window, much of the returned range does not

actually overlap.  This does not damage transform orthogonality.  Pay

attention however to returning the correct data range; the amount of

data to be returned is:

\begin{programlisting}

window_blocksize(previous_window)/4+window_blocksize(current_window)/4

\end{programlisting}

from the center (element windowsize/2) of the previous window to the

center (element windowsize/2-1, inclusive) of the current window.

Data is not returned from the first frame; it must be used to 'prime'

the decode engine.  The encoder accounts for this priming when

calculating PCM offsets; after the first frame, the proper PCM output

offset is '0' (as no data has been returned yet).

\subsubsection{output channel order}

Vorbis I specifies only a channel mapping type 0.  In mapping type 0,

channel mapping is implicitly defined as follows for standard audio

applications. As of revision 16781 (20100113), the specification adds

defined channel locations for 6.1 and 7.1 surround.  Ordering/location

for greater-than-eight channels remains 'left to the implementation'.

These channel orderings refer to order within the encoded stream.  It

is naturally possible for a decoder to produce output with channels in

any order. Any such decoder should explicitly document channel

reordering behavior.

\begin{description} %[style=nextline]

 \item[one channel]

	the stream is monophonic

\item[two channels]

	the stream is stereo.  channel order: left, right

\item[three channels]

	the stream is a 1d-surround encoding.  channel order: left,

center, right

\item[four channels]

	the stream is quadraphonic surround.  channel order: front left,

front right, rear left, rear right

\item[five channels]

	the stream is five-channel surround.  channel order: front left,

center, front right, rear left, rear right

\item[six channels]

	the stream is 5.1 surround.  channel order: front left, center, 

front right, rear left, rear right, LFE

\item[seven channels]

        the stream is 6.1 surround.  channel order: front left, center, 

front right, side left, side right, rear center, LFE

\item[eight channels]

        the stream is 7.1 surround.  channel order: front left, center, 

front right, side left, side right, rear left, rear right, 

LFE

\item[greater than eight channels]

	channel use and order is defined by the application

\end{description}

Applications using Vorbis for dedicated purposes may define channel

mapping as seen fit.  Future channel mappings (such as three and four

channel \href{http://www.ambisonic.net/}{Ambisonics}) will

make use of channel mappings other than mapping 0.