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    1 <?xml version="1.0" standalone="no"?>
    2 <!DOCTYPE section PUBLIC "-//OASIS//DTD DocBook XML V4.2//EN"
    3                 "http://www.oasis-open.org/docbook/xml/4.2/docbookx.dtd" [
    4 
    5 ]>
    6 
    7 <section id="vorbis-spec-intro">
    8 <sectioninfo>
    9 <releaseinfo>
   10  $Id: 01-introduction.xml 7186 2004-07-20 07:19:25Z xiphmont $
   11 </releaseinfo>
   12 </sectioninfo>
   13 <title>Introduction and Description</title>
   14 
   15 <section>
   16 <title>Overview</title>
   17 
   18 <para>
   19 This document provides a high level description of the Vorbis codec's
   20 construction.  A bit-by-bit specification appears beginning in 
   21 <xref linkend="vorbis-spec-codec"/>.
   22 The later sections assume a high-level
   23 understanding of the Vorbis decode process, which is 
   24 provided here.</para>
   25 
   26 <section>
   27 <title>Application</title>
   28 <para>
   29 Vorbis is a general purpose perceptual audio CODEC intended to allow
   30 maximum encoder flexibility, thus allowing it to scale competitively
   31 over an exceptionally wide range of bitrates.  At the high
   32 quality/bitrate end of the scale (CD or DAT rate stereo, 16/24 bits)
   33 it is in the same league as MPEG-2 and MPC.  Similarly, the 1.0
   34 encoder can encode high-quality CD and DAT rate stereo at below 48kbps
   35 without resampling to a lower rate.  Vorbis is also intended for
   36 lower and higher sample rates (from 8kHz telephony to 192kHz digital
   37 masters) and a range of channel representations (monaural,
   38 polyphonic, stereo, quadraphonic, 5.1, ambisonic, or up to 255
   39 discrete channels).
   40 </para>
   41 </section>
   42 
   43 <section>
   44 <title>Classification</title>
   45 <para>
   46 Vorbis I is a forward-adaptive monolithic transform CODEC based on the
   47 Modified Discrete Cosine Transform.  The codec is structured to allow
   48 addition of a hybrid wavelet filterbank in Vorbis II to offer better
   49 transient response and reproduction using a transform better suited to
   50 localized time events.
   51 </para>
   52 </section>
   53 
   54 <section>
   55 <title>Assumptions</title>
   56 
   57 <para>
   58 The Vorbis CODEC design assumes a complex, psychoacoustically-aware
   59 encoder and simple, low-complexity decoder. Vorbis decode is
   60 computationally simpler than mp3, although it does require more
   61 working memory as Vorbis has no static probability model; the vector
   62 codebooks used in the first stage of decoding from the bitstream are
   63 packed in their entirety into the Vorbis bitstream headers. In
   64 packed form, these codebooks occupy only a few kilobytes; the extent
   65 to which they are pre-decoded into a cache is the dominant factor in
   66 decoder memory usage.
   67 </para>
   68 
   69 <para>
   70 Vorbis provides none of its own framing, synchronization or protection
   71 against errors; it is solely a method of accepting input audio,
   72 dividing it into individual frames and compressing these frames into
   73 raw, unformatted 'packets'. The decoder then accepts these raw
   74 packets in sequence, decodes them, synthesizes audio frames from
   75 them, and reassembles the frames into a facsimile of the original
   76 audio stream. Vorbis is a free-form variable bit rate (VBR) codec and packets have no
   77 minimum size, maximum size, or fixed/expected size.  Packets
   78 are designed that they may be truncated (or padded) and remain
   79 decodable; this is not to be considered an error condition and is used
   80 extensively in bitrate management in peeling.  Both the transport
   81 mechanism and decoder must allow that a packet may be any size, or
   82 end before or after packet decode expects.</para>
   83 
   84 <para>
   85 Vorbis packets are thus intended to be used with a transport mechanism
   86 that provides free-form framing, sync, positioning and error correction
   87 in accordance with these design assumptions, such as Ogg (for file
   88 transport) or RTP (for network multicast).  For purposes of a few
   89 examples in this document, we will assume that Vorbis is to be
   90 embedded in an Ogg stream specifically, although this is by no means a
   91 requirement or fundamental assumption in the Vorbis design.</para>
   92 
   93 <para>
   94 The specification for embedding Vorbis into
   95 an Ogg transport stream is in <xref linkend="vorbis-over-ogg"/>.
   96 </para>
   97 
   98 </section>
   99 
  100 <section>
  101 <title>Codec Setup and Probability Model</title>
  102 
  103 <para>
  104 Vorbis' heritage is as a research CODEC and its current design
  105 reflects a desire to allow multiple decades of continuous encoder
  106 improvement before running out of room within the codec specification.
  107 For these reasons, configurable aspects of codec setup intentionally
  108 lean toward the extreme of forward adaptive.</para>
  109 
  110 <para>
  111 The single most controversial design decision in Vorbis (and the most
  112 unusual for a Vorbis developer to keep in mind) is that the entire
  113 probability model of the codec, the Huffman and VQ codebooks, is
  114 packed into the bitstream header along with extensive CODEC setup
  115 parameters (often several hundred fields).  This makes it impossible,
  116 as it would be with MPEG audio layers, to embed a simple frame type
  117 flag in each audio packet, or begin decode at any frame in the stream
  118 without having previously fetched the codec setup header.
  119 </para>
  120 
  121 <note><para>
  122 Vorbis <emphasis>can</emphasis> initiate decode at any arbitrary packet within a
  123 bitstream so long as the codec has been initialized/setup with the
  124 setup headers.</para></note>
  125 
  126 <para>
  127 Thus, Vorbis headers are both required for decode to begin and
  128 relatively large as bitstream headers go.  The header size is
  129 unbounded, although for streaming a rule-of-thumb of 4kB or less is
  130 recommended (and Xiph.Org's Vorbis encoder follows this suggestion).</para>
  131 
  132 <para>
  133 Our own design work indicates the primary liability of the
  134 required header is in mindshare; it is an unusual design and thus
  135 causes some amount of complaint among engineers as this runs against
  136 current design trends (and also points out limitations in some
  137 existing software/interface designs, such as Windows' ACM codec
  138 framework).  However, we find that it does not fundamentally limit
  139 Vorbis' suitable application space.</para>
  140 
  141 </section>
  142 
  143 <section><title>Format Specification</title>
  144 <para>
  145 The Vorbis format is well-defined by its decode specification; any
  146 encoder that produces packets that are correctly decoded by the
  147 reference Vorbis decoder described below may be considered a proper
  148 Vorbis encoder.  A decoder must faithfully and completely implement
  149 the specification defined below (except where noted) to be considered
  150 a proper Vorbis decoder.</para>
  151 </section>
  152 
  153 <section><title>Hardware Profile</title>
  154 <para>
  155 Although Vorbis decode is computationally simple, it may still run
  156 into specific limitations of an embedded design.  For this reason,
  157 embedded designs are allowed to deviate in limited ways from the
  158 'full' decode specification yet still be certified compliant.  These
  159 optional omissions are labelled in the spec where relevant.</para>
  160 </section>
  161 
  162 </section>
  163 
  164 <section>
  165 <title>Decoder Configuration</title>
  166 
  167 <para>
  168 Decoder setup consists of configuration of multiple, self-contained
  169 component abstractions that perform specific functions in the decode
  170 pipeline.  Each different component instance of a specific type is
  171 semantically interchangeable; decoder configuration consists both of
  172 internal component configuration, as well as arrangement of specific
  173 instances into a decode pipeline.  Componentry arrangement is roughly
  174 as follows:</para>
  175 
  176 <mediaobject>
  177 <imageobject>
  178  <imagedata fileref="components.png" format="PNG"/>
  179 </imageobject>
  180 <textobject>
  181   <phrase>decoder pipeline configuration</phrase>
  182 </textobject>
  183 </mediaobject>
  184 
  185 <section><title>Global Config</title>
  186 <para>
  187 Global codec configuration consists of a few audio related fields
  188 (sample rate, channels), Vorbis version (always '0' in Vorbis I),
  189 bitrate hints, and the lists of component instances.  All other
  190 configuration is in the context of specific components.</para>
  191 </section>
  192 
  193 <section><title>Mode</title>
  194 
  195 <para>
  196 Each Vorbis frame is coded according to a master 'mode'.  A bitstream
  197 may use one or many modes.</para>
  198 
  199 <para>
  200 The mode mechanism is used to encode a frame according to one of
  201 multiple possible methods with the intention of choosing a method best
  202 suited to that frame.  Different modes are, e.g. how frame size
  203 is changed from frame to frame. The mode number of a frame serves as a
  204 top level configuration switch for all other specific aspects of frame
  205 decode.</para>
  206 
  207 <para>
  208 A 'mode' configuration consists of a frame size setting, window type
  209 (always 0, the Vorbis window, in Vorbis I), transform type (always
  210 type 0, the MDCT, in Vorbis I) and a mapping number.  The mapping
  211 number specifies which mapping configuration instance to use for
  212 low-level packet decode and synthesis.</para>
  213 
  214 </section>
  215 
  216 <section><title>Mapping</title>
  217 
  218 <para>
  219 A mapping contains a channel coupling description and a list of
  220 'submaps' that bundle sets of channel vectors together for grouped
  221 encoding and decoding. These submaps are not references to external
  222 components; the submap list is internal and specific to a mapping.</para>
  223 
  224 <para>
  225 A 'submap' is a configuration/grouping that applies to a subset of
  226 floor and residue vectors within a mapping.  The submap functions as a
  227 last layer of indirection such that specific special floor or residue
  228 settings can be applied not only to all the vectors in a given mode,
  229 but also specific vectors in a specific mode.  Each submap specifies
  230 the proper floor and residue instance number to use for decoding that
  231 submap's spectral floor and spectral residue vectors.</para>
  232 
  233 <para>
  234 As an example:</para>
  235 
  236 <para>
  237 Assume a Vorbis stream that contains six channels in the standard 5.1
  238 format.  The sixth channel, as is normal in 5.1, is bass only.
  239 Therefore it would be wasteful to encode a full-spectrum version of it
  240 as with the other channels.  The submapping mechanism can be used to
  241 apply a full range floor and residue encoding to channels 0 through 4,
  242 and a bass-only representation to the bass channel, thus saving space.
  243 In this example, channels 0-4 belong to submap 0 (which indicates use
  244 of a full-range floor) and channel 5 belongs to submap 1, which uses a
  245 bass-only representation.</para>
  246 
  247 </section>
  248 
  249 <section><title>Floor</title>
  250 
  251 <para>
  252 Vorbis encodes a spectral 'floor' vector for each PCM channel.  This
  253 vector is a low-resolution representation of the audio spectrum for
  254 the given channel in the current frame, generally used akin to a
  255 whitening filter.  It is named a 'floor' because the Xiph.Org
  256 reference encoder has historically used it as a unit-baseline for
  257 spectral resolution.</para>
  258 
  259 <para>
  260 A floor encoding may be of two types.  Floor 0 uses a packed LSP
  261 representation on a dB amplitude scale and Bark frequency scale.
  262 Floor 1 represents the curve as a piecewise linear interpolated
  263 representation on a dB amplitude scale and linear frequency scale.
  264 The two floors are semantically interchangeable in
  265 encoding/decoding. However, floor type 1 provides more stable
  266 inter-frame behavior, and so is the preferred choice in all
  267 coupled-stereo and high bitrate modes.  Floor 1 is also considerably
  268 less expensive to decode than floor 0.</para>
  269 
  270 <para>
  271 Floor 0 is not to be considered deprecated, but it is of limited
  272 modern use.  No known Vorbis encoder past Xiph.org's own beta 4 makes
  273 use of floor 0.</para>
  274 
  275 <para>
  276 The values coded/decoded by a floor are both compactly formatted and
  277 make use of entropy coding to save space.  For this reason, a floor
  278 configuration generally refers to multiple codebooks in the codebook
  279 component list.  Entropy coding is thus provided as an abstraction,
  280 and each floor instance may choose from any and all available
  281 codebooks when coding/decoding.</para>
  282 
  283 </section>
  284 
  285 <section><title>Residue</title>
  286 <para>
  287 The spectral residue is the fine structure of the audio spectrum
  288 once the floor curve has been subtracted out.  In simplest terms, it
  289 is coded in the bitstream using cascaded (multi-pass) vector
  290 quantization according to one of three specific packing/coding
  291 algorithms numbered 0 through 2.  The packing algorithm details are
  292 configured by residue instance.  As with the floor components, the
  293 final VQ/entropy encoding is provided by external codebook instances
  294 and each residue instance may choose from any and all available
  295 codebooks.</para>
  296 </section>
  297 
  298 <section><title>Codebooks</title>
  299 
  300 <para>
  301 Codebooks are a self-contained abstraction that perform entropy
  302 decoding and, optionally, use the entropy-decoded integer value as an
  303 offset into an index of output value vectors, returning the indicated
  304 vector of values.</para>
  305 
  306 <para>
  307 The entropy coding in a Vorbis I codebook is provided by a standard
  308 Huffman binary tree representation.  This tree is tightly packed using
  309 one of several methods, depending on whether codeword lengths are
  310 ordered or unordered, or the tree is sparse.</para>
  311 
  312 <para>
  313 The codebook vector index is similarly packed according to index
  314 characteristic.  Most commonly, the vector index is encoded as a
  315 single list of values of possible values that are then permuted into
  316 a list of n-dimensional rows (lattice VQ).</para>
  317 
  318 </section>
  319 
  320 </section>
  321 
  322 
  323 <section>
  324 <title>High-level Decode Process</title>
  325 
  326 <section>
  327 <title>Decode Setup</title> 
  328 
  329 <para>
  330 Before decoding can begin, a decoder must initialize using the
  331 bitstream headers matching the stream to be decoded.  Vorbis uses
  332 three header packets; all are required, in-order, by this
  333 specification. Once set up, decode may begin at any audio packet
  334 belonging to the Vorbis stream. In Vorbis I, all packets after the
  335 three initial headers are audio packets. </para>
  336 
  337 <para>
  338 The header packets are, in order, the identification
  339 header, the comments header, and the setup header.</para>
  340 
  341 <section><title>Identification Header</title>
  342 <para>
  343 The identification header identifies the bitstream as Vorbis, Vorbis
  344 version, and the simple audio characteristics of the stream such as
  345 sample rate and number of channels.</para>
  346 </section>
  347 
  348 <section><title>Comment Header</title>
  349 <para>
  350 The comment header includes user text comments ("tags") and a vendor
  351 string for the application/library that produced the bitstream.  The
  352 encoding and proper use of the comment header is described in 
  353 <xref linkend="vorbis-spec-comment"/>.</para>
  354 </section>
  355 
  356 <section><title>Setup Header</title>
  357 <para>
  358 The setup header includes extensive CODEC setup information as well as
  359 the complete VQ and Huffman codebooks needed for decode.</para>
  360 </section>
  361 
  362 </section>
  363 
  364 <section><title>Decode Procedure</title>
  365 
  366 <highlights>
  367 <para>
  368 The decoding and synthesis procedure for all audio packets is
  369 fundamentally the same.
  370 <orderedlist>
  371 <listitem><simpara>decode packet type flag</simpara></listitem>
  372 <listitem><simpara>decode mode number</simpara></listitem>
  373 <listitem><simpara>decode window shape (long windows only)</simpara></listitem>
  374 <listitem><simpara>decode floor</simpara></listitem>
  375 <listitem><simpara>decode residue into residue vectors</simpara></listitem>
  376 <listitem><simpara>inverse channel coupling of residue vectors</simpara></listitem>
  377 <listitem><simpara>generate floor curve from decoded floor data</simpara></listitem>
  378 <listitem><simpara>compute dot product of floor and residue, producing audio spectrum vector</simpara></listitem>
  379 <listitem><simpara>inverse monolithic transform of audio spectrum vector, always an MDCT in Vorbis I</simpara></listitem>
  380 <listitem><simpara>overlap/add left-hand output of transform with right-hand output of previous frame</simpara></listitem>
  381 <listitem><simpara>store right hand-data from transform of current frame for future lapping</simpara></listitem>
  382 <listitem><simpara>if not first frame, return results of overlap/add as audio result of current frame</simpara></listitem>
  383 </orderedlist>
  384 </para>
  385 </highlights>
  386 
  387 <para>
  388 Note that clever rearrangement of the synthesis arithmetic is
  389 possible; as an example, one can take advantage of symmetries in the
  390 MDCT to store the right-hand transform data of a partial MDCT for a
  391 50% inter-frame buffer space savings, and then complete the transform
  392 later before overlap/add with the next frame.  This optimization
  393 produces entirely equivalent output and is naturally perfectly legal.
  394 The decoder must be <emphasis>entirely mathematically equivalent</emphasis> to the
  395 specification, it need not be a literal semantic implementation.</para>
  396 
  397 <section><title>Packet type decode</title> 
  398 
  399 <para>
  400 Vorbis I uses four packet types. The first three packet types mark each
  401 of the three Vorbis headers described above. The fourth packet type
  402 marks an audio packet. All other packet types are reserved; packets
  403 marked with a reserved type should be ignored.</para>
  404 
  405 <para>
  406 Following the three header packets, all packets in a Vorbis I stream
  407 are audio.  The first step of audio packet decode is to read and
  408 verify the packet type; <emphasis>a non-audio packet when audio is expected
  409 indicates stream corruption or a non-compliant stream. The decoder
  410 must ignore the packet and not attempt decoding it to
  411 audio</emphasis>.</para>
  412 
  413 </section>
  414 
  415 
  416 <section><title>Mode decode</title>
  417 <para>
  418 Vorbis allows an encoder to set up multiple, numbered packet 'modes',
  419 as described earlier, all of which may be used in a given Vorbis
  420 stream. The mode is encoded as an integer used as a direct offset into
  421 the mode instance index. </para>
  422 </section>
  423 
  424 <section id="vorbis-spec-window">
  425 <title>Window shape decode (long windows only)</title>
  426 
  427 <para>
  428 Vorbis frames may be one of two PCM sample sizes specified during
  429 codec setup.  In Vorbis I, legal frame sizes are powers of two from 64
  430 to 8192 samples.  Aside from coupling, Vorbis handles channels as
  431 independent vectors and these frame sizes are in samples per channel.</para>
  432 
  433 <para>
  434 Vorbis uses an overlapping transform, namely the MDCT, to blend one
  435 frame into the next, avoiding most inter-frame block boundary
  436 artifacts.  The MDCT output of one frame is windowed according to MDCT
  437 requirements, overlapped 50% with the output of the previous frame and
  438 added.  The window shape assures seamless reconstruction.  </para>
  439 
  440 <para>
  441 This is easy to visualize in the case of equal sized-windows:</para>
  442 
  443 <mediaobject>
  444 <imageobject>
  445  <imagedata fileref="window1.png" format="PNG"/>
  446 </imageobject>
  447 <textobject>
  448  <phrase>overlap of two equal-sized windows</phrase>
  449 </textobject>
  450 </mediaobject>
  451 
  452 <para>
  453 And slightly more complex in the case of overlapping unequal sized
  454 windows:</para>
  455 
  456 <mediaobject>
  457 <imageobject> 
  458  <imagedata fileref="window2.png" format="PNG"/>
  459 </imageobject>
  460 <textobject>
  461  <phrase>overlap of a long and a short window</phrase>
  462 </textobject>
  463 </mediaobject>
  464 
  465 <para>
  466 In the unequal-sized window case, the window shape of the long window
  467 must be modified for seamless lapping as above.  It is possible to
  468 correctly infer window shape to be applied to the current window from
  469 knowing the sizes of the current, previous and next window.  It is
  470 legal for a decoder to use this method. However, in the case of a long
  471 window (short windows require no modification), Vorbis also codes two
  472 flag bits to specify pre- and post- window shape.  Although not
  473 strictly necessary for function, this minor redundancy allows a packet
  474 to be fully decoded to the point of lapping entirely independently of
  475 any other packet, allowing easier abstraction of decode layers as well
  476 as allowing a greater level of easy parallelism in encode and
  477 decode.</para>
  478 
  479 <para>
  480 A description of valid window functions for use with an inverse MDCT
  481 can be found in the paper 
  482 <citetitle pubwork="article">
  483 <ulink url="http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps">
  484 The use of multirate filter banks for coding of high quality digital
  485 audio</ulink></citetitle>, by T. Sporer, K. Brandenburg and B. Edler.  Vorbis windows
  486 all use the slope function 
  487   <inlineequation>
  488 
  489     <alt>y=sin(.5*PI*sin^2((x+.5)/n*pi))</alt>
  490     <inlinemediaobject>
  491      <textobject>
  492       <phrase>$y = \sin(.5*\pi \, \sin^2((x+.5)/n*\pi))$</phrase>
  493      </textobject>
  494     </inlinemediaobject>
  495   </inlineequation>.
  496 </para>
  497 
  498 </section>
  499 
  500 <section><title>floor decode</title>
  501 <para>
  502 Each floor is encoded/decoded in channel order, however each floor
  503 belongs to a 'submap' that specifies which floor configuration to
  504 use.  All floors are decoded before residue decode begins.</para>
  505 </section>
  506 
  507 <section><title>residue decode</title> 
  508 
  509 <para>
  510 Although the number of residue vectors equals the number of channels,
  511 channel coupling may mean that the raw residue vectors extracted
  512 during decode do not map directly to specific channels.  When channel
  513 coupling is in use, some vectors will correspond to coupled magnitude
  514 or angle.  The coupling relationships are described in the codec setup
  515 and may differ from frame to frame, due to different mode numbers.</para>
  516 
  517 <para>
  518 Vorbis codes residue vectors in groups by submap; the coding is done
  519 in submap order from submap 0 through n-1.  This differs from floors
  520 which are coded using a configuration provided by submap number, but
  521 are coded individually in channel order.</para>
  522 
  523 </section>
  524 
  525 <section><title>inverse channel coupling</title>
  526 
  527 <para>
  528 A detailed discussion of stereo in the Vorbis codec can be found in
  529 the document <ulink url="stereo.html"><citetitle>Stereo Channel Coupling in the
  530 Vorbis CODEC</citetitle></ulink>.  Vorbis is not limited to only stereo coupling, but
  531 the stereo document also gives a good overview of the generic coupling
  532 mechanism.</para>
  533 
  534 <para>
  535 Vorbis coupling applies to pairs of residue vectors at a time;
  536 decoupling is done in-place a pair at a time in the order and using
  537 the vectors specified in the current mapping configuration.  The
  538 decoupling operation is the same for all pairs, converting square
  539 polar representation (where one vector is magnitude and the second
  540 angle) back to Cartesian representation.</para>
  541 
  542 <para>
  543 After decoupling, in order, each pair of vectors on the coupling list, 
  544 the resulting residue vectors represent the fine spectral detail
  545 of each output channel.</para>
  546 
  547 </section>
  548 
  549 <section><title>generate floor curve</title>
  550 
  551 <para>
  552 The decoder may choose to generate the floor curve at any appropriate
  553 time.  It is reasonable to generate the output curve when the floor
  554 data is decoded from the raw packet, or it can be generated after
  555 inverse coupling and applied to the spectral residue directly,
  556 combining generation and the dot product into one step and eliminating
  557 some working space.</para>
  558 
  559 <para>
  560 Both floor 0 and floor 1 generate a linear-range, linear-domain output
  561 vector to be multiplied (dot product) by the linear-range,
  562 linear-domain spectral residue.</para>
  563 
  564 </section>
  565 
  566 <section><title>compute floor/residue dot product</title>
  567 
  568 <para>
  569 This step is straightforward; for each output channel, the decoder
  570 multiplies the floor curve and residue vectors element by element,
  571 producing the finished audio spectrum of each channel.</para>
  572 
  573 <para>
  574 One point is worth mentioning about this dot product; a common mistake
  575 in a fixed point implementation might be to assume that a 32 bit
  576 fixed-point representation for floor and residue and direct
  577 multiplication of the vectors is sufficient for acceptable spectral
  578 depth in all cases because it happens to mostly work with the current
  579 Xiph.Org reference encoder.</para>
  580 
  581 <para>
  582 However, floor vector values can span ~140dB (~24 bits unsigned), and
  583 the audio spectrum vector should represent a minimum of 120dB (~21
  584 bits with sign), even when output is to a 16 bit PCM device.  For the
  585 residue vector to represent full scale if the floor is nailed to
  586 -140dB, it must be able to span 0 to +140dB.  For the residue vector
  587 to reach full scale if the floor is nailed at 0dB, it must be able to
  588 represent -140dB to +0dB.  Thus, in order to handle full range
  589 dynamics, a residue vector may span -140dB to +140dB entirely within
  590 spec.  A 280dB range is approximately 48 bits with sign; thus the
  591 residue vector must be able to represent a 48 bit range and the dot
  592 product must be able to handle an effective 48 bit times 24 bit
  593 multiplication.  This range may be achieved using large (64 bit or
  594 larger) integers, or implementing a movable binary point
  595 representation.</para>
  596 
  597 </section>
  598 
  599 <section><title>inverse monolithic transform (MDCT)</title>
  600 
  601 <para>
  602 The audio spectrum is converted back into time domain PCM audio via an
  603 inverse Modified Discrete Cosine Transform (MDCT).  A detailed
  604 description of the MDCT is available in the paper <ulink
  605 url="http://www.iocon.com/resource/docs/ps/eusipco_corrected.ps"><citetitle pubwork="article">The use of multirate filter banks for coding of high quality digital
  606 audio</citetitle></ulink>, by T. Sporer, K. Brandenburg and B. Edler.</para>
  607 
  608 <para>
  609 Note that the PCM produced directly from the MDCT is not yet finished
  610 audio; it must be lapped with surrounding frames using an appropriate
  611 window (such as the Vorbis window) before the MDCT can be considered
  612 orthogonal.</para>
  613 
  614 </section>
  615 
  616 <section><title>overlap/add data</title>
  617 <para>
  618 Windowed MDCT output is overlapped and added with the right hand data
  619 of the previous window such that the 3/4 point of the previous window
  620 is aligned with the 1/4 point of the current window (as illustrated in
  621 the window overlap diagram). At this point, the audio data between the
  622 center of the previous frame and the center of the current frame is
  623 now finished and ready to be returned. </para>
  624 </section>
  625 
  626 <section><title>cache right hand data</title>
  627 <para>
  628 The decoder must cache the right hand portion of the current frame to
  629 be lapped with the left hand portion of the next frame.
  630 </para>
  631 </section>
  632 
  633 <section><title>return finished audio data</title>
  634 
  635 <para>
  636 The overlapped portion produced from overlapping the previous and
  637 current frame data is finished data to be returned by the decoder.
  638 This data spans from the center of the previous window to the center
  639 of the current window.  In the case of same-sized windows, the amount
  640 of data to return is one-half block consisting of and only of the
  641 overlapped portions. When overlapping a short and long window, much of
  642 the returned range is not actually overlap.  This does not damage
  643 transform orthogonality.  Pay attention however to returning the
  644 correct data range; the amount of data to be returned is:
  645 
  646 <programlisting>
  647 window_blocksize(previous_window)/4+window_blocksize(current_window)/4
  648 </programlisting>
  649 
  650 from the center of the previous window to the center of the current
  651 window.</para>
  652 
  653 <para>
  654 Data is not returned from the first frame; it must be used to 'prime'
  655 the decode engine.  The encoder accounts for this priming when
  656 calculating PCM offsets; after the first frame, the proper PCM output
  657 offset is '0' (as no data has been returned yet).</para>
  658 </section>
  659 </section>
  660 
  661 </section>
  662 
  663 </section>
  664 <!-- end Vorbis I specification introduction and description -->
  665