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- <a href="http://www.xiph.org/"><img src="fish_xiph_org.png" alt="Fish Logo and Xiph.org"/></a>\r
-</div>\r
-\r
-<h1>Ogg Vorbis stereo-specific channel coupling discussion</h1>\r
-\r
-<h2>Abstract</h2>\r
-\r
-<p>The Vorbis audio CODEC provides a channel coupling\r
-mechanisms designed to reduce effective bitrate by both eliminating\r
-interchannel redundancy and eliminating stereo image information\r
-labeled inaudible or undesirable according to spatial psychoacoustic\r
-models. This document describes both the mechanical coupling\r
-mechanisms available within the Vorbis specification, as well as the\r
-specific stereo coupling models used by the reference\r
-<tt>libvorbis</tt> codec provided by xiph.org.</p>\r
-\r
-<h2>Mechanisms</h2>\r
-\r
-<p>In encoder release beta 4 and earlier, Vorbis supported multiple\r
-channel encoding, but the channels were encoded entirely separately\r
-with no cross-analysis or redundancy elimination between channels.\r
-This multichannel strategy is very similar to the mp3's <em>dual\r
-stereo</em> mode and Vorbis uses the same name for its analogous\r
-uncoupled multichannel modes.</p>\r
-\r
-<p>However, the Vorbis spec provides for, and Vorbis release 1.0 rc1 and\r
-later implement a coupled channel strategy. Vorbis has two specific\r
-mechanisms that may be used alone or in conjunction to implement\r
-channel coupling. The first is <em>channel interleaving</em> via\r
-residue backend type 2, and the second is <em>square polar\r
-mapping</em>. These two general mechanisms are particularly well\r
-suited to coupling due to the structure of Vorbis encoding, as we'll\r
-explore below, and using both we can implement both totally\r
-<em>lossless stereo image coupling</em> [bit-for-bit decode-identical\r
-to uncoupled modes], as well as various lossy models that seek to\r
-eliminate inaudible or unimportant aspects of the stereo image in\r
-order to enhance bitrate. The exact coupling implementation is\r
-generalized to allow the encoder a great deal of flexibility in\r
-implementation of a stereo or surround model without requiring any\r
-significant complexity increase over the combinatorially simpler\r
-mid/side joint stereo of mp3 and other current audio codecs.</p>\r
-\r
-<p>A particular Vorbis bitstream may apply channel coupling directly to\r
-more than a pair of channels; polar mapping is hierarchical such that\r
-polar coupling may be extrapolated to an arbitrary number of channels\r
-and is not restricted to only stereo, quadraphonics, ambisonics or 5.1\r
-surround. However, the scope of this document restricts itself to the\r
-stereo coupling case.</p>\r
-\r
-<h3>Square Polar Mapping</h3>\r
-\r
-<h4>maximal correlation</h4>\r
- \r
-<p>Recall that the basic structure of a a Vorbis I stream first generates\r
-from input audio a spectral 'floor' function that serves as an\r
-MDCT-domain whitening filter. This floor is meant to represent the\r
-rough envelope of the frequency spectrum, using whatever metric the\r
-encoder cares to define. This floor is subtracted from the log\r
-frequency spectrum, effectively normalizing the spectrum by frequency.\r
-Each input channel is associated with a unique floor function.</p>\r
-\r
-<p>The basic idea behind any stereo coupling is that the left and right\r
-channels usually correlate. This correlation is even stronger if one\r
-first accounts for energy differences in any given frequency band\r
-across left and right; think for example of individual instruments\r
-mixed into different portions of the stereo image, or a stereo\r
-recording with a dominant feature not perfectly in the center. The\r
-floor functions, each specific to a channel, provide the perfect means\r
-of normalizing left and right energies across the spectrum to maximize\r
-correlation before coupling. This feature of the Vorbis format is not\r
-a convenient accident.</p>\r
-\r
-<p>Because we strive to maximally correlate the left and right channels\r
-and generally succeed in doing so, left and right residue is typically\r
-nearly identical. We could use channel interleaving (discussed below)\r
-alone to efficiently remove the redundancy between the left and right\r
-channels as a side effect of entropy encoding, but a polar\r
-representation gives benefits when left/right correlation is\r
-strong.</p>\r
-\r
-<h4>point and diffuse imaging</h4>\r
-\r
-<p>The first advantage of a polar representation is that it effectively\r
-separates the spatial audio information into a 'point image'\r
-(magnitude) at a given frequency and located somewhere in the sound\r
-field, and a 'diffuse image' (angle) that fills a large amount of\r
-space simultaneously. Even if we preserve only the magnitude (point)\r
-data, a detailed and carefully chosen floor function in each channel\r
-provides us with a free, fine-grained, frequency relative intensity\r
-stereo*. Angle information represents diffuse sound fields, such as\r
-reverberation that fills the entire space simultaneously.</p>\r
-\r
-<p>*<em>Because the Vorbis model supports a number of different possible\r
-stereo models and these models may be mixed, we do not use the term\r
-'intensity stereo' talking about Vorbis; instead we use the terms\r
-'point stereo', 'phase stereo' and subcategories of each.</em></p>\r
-\r
-<p>The majority of a stereo image is representable by polar magnitude\r
-alone, as strong sounds tend to be produced at near-point sources;\r
-even non-diffuse, fast, sharp echoes track very accurately using\r
-magnitude representation almost alone (for those experimenting with\r
-Vorbis tuning, this strategy works much better with the precise,\r
-piecewise control of floor 1; the continuous approximation of floor 0\r
-results in unstable imaging). Reverberation and diffuse sounds tend\r
-to contain less energy and be psychoacoustically dominated by the\r
-point sources embedded in them. Thus, we again tend to concentrate\r
-more represented energy into a predictably smaller number of numbers.\r
-Separating representation of point and diffuse imaging also allows us\r
-to model and manipulate point and diffuse qualities separately.</p>\r
-\r
-<h4>controlling bit leakage and symbol crosstalk</h4>\r
-\r
-<p>Because polar\r
-representation concentrates represented energy into fewer large\r
-values, we reduce bit 'leakage' during cascading (multistage VQ\r
-encoding) as a secondary benefit. A single large, monolithic VQ\r
-codebook is more efficient than a cascaded book due to entropy\r
-'crosstalk' among symbols between different stages of a multistage cascade.\r
-Polar representation is a way of further concentrating entropy into\r
-predictable locations so that codebook design can take steps to\r
-improve multistage codebook efficiency. It also allows us to cascade\r
-various elements of the stereo image independently.</p>\r
-\r
-<h4>eliminating trigonometry and rounding</h4>\r
-\r
-<p>Rounding and computational complexity are potential problems with a\r
-polar representation. As our encoding process involves quantization,\r
-mixing a polar representation and quantization makes it potentially\r
-impossible, depending on implementation, to construct a coupled stereo\r
-mechanism that results in bit-identical decompressed output compared\r
-to an uncoupled encoding should the encoder desire it.</p>\r
-\r
-<p>Vorbis uses a mapping that preserves the most useful qualities of\r
-polar representation, relies only on addition/subtraction (during\r
-decode; high quality encoding still requires some trig), and makes it\r
-trivial before or after quantization to represent an angle/magnitude\r
-through a one-to-one mapping from possible left/right value\r
-permutations. We do this by basing our polar representation on the\r
-unit square rather than the unit-circle.</p>\r
-\r
-<p>Given a magnitude and angle, we recover left and right using the\r
-following function (note that A/B may be left/right or right/left\r
-depending on the coupling definition used by the encoder):</p>\r
-\r
-<pre>\r
- if(magnitude>0)\r
- if(angle>0){\r
- A=magnitude;\r
- B=magnitude-angle;\r
- }else{\r
- B=magnitude;\r
- A=magnitude+angle;\r
- }\r
- else\r
- if(angle>0){\r
- A=magnitude;\r
- B=magnitude+angle;\r
- }else{\r
- B=magnitude;\r
- A=magnitude-angle;\r
- }\r
- }\r
-</pre>\r
-\r
-<p>The function is antisymmetric for positive and negative magnitudes in\r
-order to eliminate a redundant value when quantizing. For example, if\r
-we're quantizing to integer values, we can visualize a magnitude of 5\r
-and an angle of -2 as follows:</p>\r
-\r
-<p><img src="squarepolar.png" alt="square polar"/></p>\r
-\r
-<p>This representation loses or replicates no values; if the range of A\r
-and B are integral -5 through 5, the number of possible Cartesian\r
-permutations is 121. Represented in square polar notation, the\r
-possible values are:</p>\r
-\r
-<pre>\r
- 0, 0\r
-\r
--1,-2 -1,-1 -1, 0 -1, 1\r
-\r
- 1,-2 1,-1 1, 0 1, 1\r
-\r
--2,-4 -2,-3 -2,-2 -2,-1 -2, 0 -2, 1 -2, 2 -2, 3 \r
-\r
- 2,-4 2,-3 ... following the pattern ...\r
-\r
- ... 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 5, 7 5, 8 5, 9\r
-\r
-</pre>\r
-\r
-<p>...for a grand total of 121 possible values, the same number as in\r
-Cartesian representation (note that, for example, <tt>5,-10</tt> is\r
-the same as <tt>-5,10</tt>, so there's no reason to represent\r
-both. 2,10 cannot happen, and there's no reason to account for it.)\r
-It's also obvious that this mapping is exactly reversible.</p>\r
-\r
-<h3>Channel interleaving</h3>\r
-\r
-<p>We can remap and A/B vector using polar mapping into a magnitude/angle\r
-vector, and it's clear that, in general, this concentrates energy in\r
-the magnitude vector and reduces the amount of information to encode\r
-in the angle vector. Encoding these vectors independently with\r
-residue backend #0 or residue backend #1 will result in bitrate\r
-savings. However, there are still implicit correlations between the\r
-magnitude and angle vectors. The most obvious is that the amplitude\r
-of the angle is bounded by its corresponding magnitude value.</p>\r
-\r
-<p>Entropy coding the results, then, further benefits from the entropy\r
-model being able to compress magnitude and angle simultaneously. For\r
-this reason, Vorbis implements residue backend #2 which pre-interleaves\r
-a number of input vectors (in the stereo case, two, A and B) into a\r
-single output vector (with the elements in the order of\r
-A_0, B_0, A_1, B_1, A_2 ... A_n-1, B_n-1) before entropy encoding. Thus\r
-each vector to be coded by the vector quantization backend consists of\r
-matching magnitude and angle values.</p>\r
-\r
-<p>The astute reader, at this point, will notice that in the theoretical\r
-case in which we can use monolithic codebooks of arbitrarily large\r
-size, we can directly interleave and encode left and right without\r
-polar mapping; in fact, the polar mapping does not appear to lend any\r
-benefit whatsoever to the efficiency of the entropy coding. In fact,\r
-it is perfectly possible and reasonable to build a Vorbis encoder that\r
-dispenses with polar mapping entirely and merely interleaves the\r
-channel. Libvorbis based encoders may configure such an encoding and\r
-it will work as intended.</p>\r
-\r
-<p>However, when we leave the ideal/theoretical domain, we notice that\r
-polar mapping does give additional practical benefits, as discussed in\r
-the above section on polar mapping and summarized again here:</p>\r
-\r
-<ul>\r
-<li>Polar mapping aids in controlling entropy 'leakage' between stages\r
-of a cascaded codebook.</li>\r
-<li>Polar mapping separates the stereo image\r
-into point and diffuse components which may be analyzed and handled\r
-differently.</li>\r
-</ul>\r
-\r
-<h2>Stereo Models</h2>\r
-\r
-<h3>Dual Stereo</h3>\r
-\r
-<p>Dual stereo refers to stereo encoding where the channels are entirely\r
-separate; they are analyzed and encoded as entirely distinct entities.\r
-This terminology is familiar from mp3.</p>\r
-\r
-<h3>Lossless Stereo</h3>\r
-\r
-<p>Using polar mapping and/or channel interleaving, it's possible to\r
-couple Vorbis channels losslessly, that is, construct a stereo\r
-coupling encoding that both saves space but also decodes\r
-bit-identically to dual stereo. OggEnc 1.0 and later uses this\r
-mode in all high-bitrate encoding.</p>\r
-\r
-<p>Overall, this stereo mode is overkill; however, it offers a safe\r
-alternative to users concerned about the slightest possible\r
-degradation to the stereo image or archival quality audio.</p>\r
-\r
-<h3>Phase Stereo</h3>\r
-\r
-<p>Phase stereo is the least aggressive means of gracefully dropping\r
-resolution from the stereo image; it affects only diffuse imaging.</p>\r
-\r
-<p>It's often quoted that the human ear is deaf to signal phase above\r
-about 4kHz; this is nearly true and a passable rule of thumb, but it\r
-can be demonstrated that even an average user can tell the difference\r
-between high frequency in-phase and out-of-phase noise. Obviously\r
-then, the statement is not entirely true. However, it's also the case\r
-that one must resort to nearly such an extreme demonstration before\r
-finding the counterexample.</p>\r
-\r
-<p>'Phase stereo' is simply a more aggressive quantization of the polar\r
-angle vector; above 4kHz it's generally quite safe to quantize noise\r
-and noisy elements to only a handful of allowed phases, or to thin the\r
-phase with respect to the magnitude. The phases of high amplitude\r
-pure tones may or may not be preserved more carefully (they are\r
-relatively rare and L/R tend to be in phase, so there is generally\r
-little reason not to spend a few more bits on them)</p>\r
-\r
-<h4>example: eight phase stereo</h4>\r
-\r
-<p>Vorbis may implement phase stereo coupling by preserving the entirety\r
-of the magnitude vector (essential to fine amplitude and energy\r
-resolution overall) and quantizing the angle vector to one of only\r
-four possible values. Given that the magnitude vector may be positive\r
-or negative, this results in left and right phase having eight\r
-possible permutation, thus 'eight phase stereo':</p>\r
-\r
-<p><img src="eightphase.png" alt="eight phase"/></p>\r
-\r
-<p>Left and right may be in phase (positive or negative), the most common\r
-case by far, or out of phase by 90 or 180 degrees.</p>\r
-\r
-<h4>example: four phase stereo</h4>\r
-\r
-<p>Similarly, four phase stereo takes the quantization one step further;\r
-it allows only in-phase and 180 degree out-out-phase signals:</p>\r
-\r
-<p><img src="fourphase.png" alt="four phase"/></p>\r
-\r
-<h3>example: point stereo</h3>\r
-\r
-<p>Point stereo eliminates the possibility of out-of-phase signal\r
-entirely. Any diffuse quality to a sound source tends to collapse\r
-inward to a point somewhere within the stereo image. A practical\r
-example would be balanced reverberations within a large, live space;\r
-normally the sound is diffuse and soft, giving a sonic impression of\r
-volume. In point-stereo, the reverberations would still exist, but\r
-sound fairly firmly centered within the image (assuming the\r
-reverberation was centered overall; if the reverberation is stronger\r
-to the left, then the point of localization in point stereo would be\r
-to the left). This effect is most noticeable at low and mid\r
-frequencies and using headphones (which grant perfect stereo\r
-separation). Point stereo is is a graceful but generally easy to\r
-detect degradation to the sound quality and is thus used in frequency\r
-ranges where it is least noticeable.</p>\r
-\r
-<h3>Mixed Stereo</h3>\r
-\r
-<p>Mixed stereo is the simultaneous use of more than one of the above\r
-stereo encoding models, generally using more aggressive modes in\r
-higher frequencies, lower amplitudes or 'nearly' in-phase sound.</p>\r
-\r
-<p>It is also the case that near-DC frequencies should be encoded using\r
-lossless coupling to avoid frame blocking artifacts.</p>\r
-\r
-<h3>Vorbis Stereo Modes</h3>\r
-\r
-<p>Vorbis, as of 1.0, uses lossless stereo and a number of mixed modes\r
-constructed out of lossless and point stereo. Phase stereo was used\r
-in the rc2 encoder, but is not currently used for simplicity's sake. It\r
-will likely be re-added to the stereo model in the future.</p>\r
-\r
-<div id="copyright">\r
- The Xiph Fish Logo is a\r
- trademark (™) of Xiph.Org.<br/>\r
-\r
- These pages © 1994 - 2005 Xiph.Org. All rights reserved.\r
-</div>\r
-\r
-</body>\r
-</html>\r
-\r
-\r
-\r
-\r
-\r
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+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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+</div>
+
+<h1>Ogg Vorbis stereo-specific channel coupling discussion</h1>
+
+<h2>Abstract</h2>
+
+<p>The Vorbis audio CODEC provides a channel coupling
+mechanisms designed to reduce effective bitrate by both eliminating
+interchannel redundancy and eliminating stereo image information
+labeled inaudible or undesirable according to spatial psychoacoustic
+models. This document describes both the mechanical coupling
+mechanisms available within the Vorbis specification, as well as the
+specific stereo coupling models used by the reference
+<tt>libvorbis</tt> codec provided by xiph.org.</p>
+
+<h2>Mechanisms</h2>
+
+<p>In encoder release beta 4 and earlier, Vorbis supported multiple
+channel encoding, but the channels were encoded entirely separately
+with no cross-analysis or redundancy elimination between channels.
+This multichannel strategy is very similar to the mp3's <em>dual
+stereo</em> mode and Vorbis uses the same name for its analogous
+uncoupled multichannel modes.</p>
+
+<p>However, the Vorbis spec provides for, and Vorbis release 1.0 rc1 and
+later implement a coupled channel strategy. Vorbis has two specific
+mechanisms that may be used alone or in conjunction to implement
+channel coupling. The first is <em>channel interleaving</em> via
+residue backend type 2, and the second is <em>square polar
+mapping</em>. These two general mechanisms are particularly well
+suited to coupling due to the structure of Vorbis encoding, as we'll
+explore below, and using both we can implement both totally
+<em>lossless stereo image coupling</em> [bit-for-bit decode-identical
+to uncoupled modes], as well as various lossy models that seek to
+eliminate inaudible or unimportant aspects of the stereo image in
+order to enhance bitrate. The exact coupling implementation is
+generalized to allow the encoder a great deal of flexibility in
+implementation of a stereo or surround model without requiring any
+significant complexity increase over the combinatorially simpler
+mid/side joint stereo of mp3 and other current audio codecs.</p>
+
+<p>A particular Vorbis bitstream may apply channel coupling directly to
+more than a pair of channels; polar mapping is hierarchical such that
+polar coupling may be extrapolated to an arbitrary number of channels
+and is not restricted to only stereo, quadraphonics, ambisonics or 5.1
+surround. However, the scope of this document restricts itself to the
+stereo coupling case.</p>
+
+<a name="sqpm"></a>
+<h3>Square Polar Mapping</h3>
+
+<h4>maximal correlation</h4>
+
+<p>Recall that the basic structure of a a Vorbis I stream first generates
+from input audio a spectral 'floor' function that serves as an
+MDCT-domain whitening filter. This floor is meant to represent the
+rough envelope of the frequency spectrum, using whatever metric the
+encoder cares to define. This floor is subtracted from the log
+frequency spectrum, effectively normalizing the spectrum by frequency.
+Each input channel is associated with a unique floor function.</p>
+
+<p>The basic idea behind any stereo coupling is that the left and right
+channels usually correlate. This correlation is even stronger if one
+first accounts for energy differences in any given frequency band
+across left and right; think for example of individual instruments
+mixed into different portions of the stereo image, or a stereo
+recording with a dominant feature not perfectly in the center. The
+floor functions, each specific to a channel, provide the perfect means
+of normalizing left and right energies across the spectrum to maximize
+correlation before coupling. This feature of the Vorbis format is not
+a convenient accident.</p>
+
+<p>Because we strive to maximally correlate the left and right channels
+and generally succeed in doing so, left and right residue is typically
+nearly identical. We could use channel interleaving (discussed below)
+alone to efficiently remove the redundancy between the left and right
+channels as a side effect of entropy encoding, but a polar
+representation gives benefits when left/right correlation is
+strong.</p>
+
+<h4>point and diffuse imaging</h4>
+
+<p>The first advantage of a polar representation is that it effectively
+separates the spatial audio information into a 'point image'
+(magnitude) at a given frequency and located somewhere in the sound
+field, and a 'diffuse image' (angle) that fills a large amount of
+space simultaneously. Even if we preserve only the magnitude (point)
+data, a detailed and carefully chosen floor function in each channel
+provides us with a free, fine-grained, frequency relative intensity
+stereo*. Angle information represents diffuse sound fields, such as
+reverberation that fills the entire space simultaneously.</p>
+
+<p>*<em>Because the Vorbis model supports a number of different possible
+stereo models and these models may be mixed, we do not use the term
+'intensity stereo' talking about Vorbis; instead we use the terms
+'point stereo', 'phase stereo' and subcategories of each.</em></p>
+
+<p>The majority of a stereo image is representable by polar magnitude
+alone, as strong sounds tend to be produced at near-point sources;
+even non-diffuse, fast, sharp echoes track very accurately using
+magnitude representation almost alone (for those experimenting with
+Vorbis tuning, this strategy works much better with the precise,
+piecewise control of floor 1; the continuous approximation of floor 0
+results in unstable imaging). Reverberation and diffuse sounds tend
+to contain less energy and be psychoacoustically dominated by the
+point sources embedded in them. Thus, we again tend to concentrate
+more represented energy into a predictably smaller number of numbers.
+Separating representation of point and diffuse imaging also allows us
+to model and manipulate point and diffuse qualities separately.</p>
+
+<h4>controlling bit leakage and symbol crosstalk</h4>
+
+<p>Because polar
+representation concentrates represented energy into fewer large
+values, we reduce bit 'leakage' during cascading (multistage VQ
+encoding) as a secondary benefit. A single large, monolithic VQ
+codebook is more efficient than a cascaded book due to entropy
+'crosstalk' among symbols between different stages of a multistage cascade.
+Polar representation is a way of further concentrating entropy into
+predictable locations so that codebook design can take steps to
+improve multistage codebook efficiency. It also allows us to cascade
+various elements of the stereo image independently.</p>
+
+<h4>eliminating trigonometry and rounding</h4>
+
+<p>Rounding and computational complexity are potential problems with a
+polar representation. As our encoding process involves quantization,
+mixing a polar representation and quantization makes it potentially
+impossible, depending on implementation, to construct a coupled stereo
+mechanism that results in bit-identical decompressed output compared
+to an uncoupled encoding should the encoder desire it.</p>
+
+<p>Vorbis uses a mapping that preserves the most useful qualities of
+polar representation, relies only on addition/subtraction (during
+decode; high quality encoding still requires some trig), and makes it
+trivial before or after quantization to represent an angle/magnitude
+through a one-to-one mapping from possible left/right value
+permutations. We do this by basing our polar representation on the
+unit square rather than the unit-circle.</p>
+
+<p>Given a magnitude and angle, we recover left and right using the
+following function (note that A/B may be left/right or right/left
+depending on the coupling definition used by the encoder):</p>
+
+<pre>
+ if(magnitude>0)
+ if(angle>0){
+ A=magnitude;
+ B=magnitude-angle;
+ }else{
+ B=magnitude;
+ A=magnitude+angle;
+ }
+ else
+ if(angle>0){
+ A=magnitude;
+ B=magnitude+angle;
+ }else{
+ B=magnitude;
+ A=magnitude-angle;
+ }
+ }
+</pre>
+
+<p>The function is antisymmetric for positive and negative magnitudes in
+order to eliminate a redundant value when quantizing. For example, if
+we're quantizing to integer values, we can visualize a magnitude of 5
+and an angle of -2 as follows:</p>
+
+<p><img src="squarepolar.png" alt="square polar"/></p>
+
+<p>This representation loses or replicates no values; if the range of A
+and B are integral -5 through 5, the number of possible Cartesian
+permutations is 121. Represented in square polar notation, the
+possible values are:</p>
+
+<pre>
+ 0, 0
+
+-1,-2 -1,-1 -1, 0 -1, 1
+
+ 1,-2 1,-1 1, 0 1, 1
+
+-2,-4 -2,-3 -2,-2 -2,-1 -2, 0 -2, 1 -2, 2 -2, 3
+
+ 2,-4 2,-3 ... following the pattern ...
+
+ ... 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 5, 7 5, 8 5, 9
+
+</pre>
+
+<p>...for a grand total of 121 possible values, the same number as in
+Cartesian representation (note that, for example, <tt>5,-10</tt> is
+the same as <tt>-5,10</tt>, so there's no reason to represent
+both. 2,10 cannot happen, and there's no reason to account for it.)
+It's also obvious that this mapping is exactly reversible.</p>
+
+<h3>Channel interleaving</h3>
+
+<p>We can remap and A/B vector using polar mapping into a magnitude/angle
+vector, and it's clear that, in general, this concentrates energy in
+the magnitude vector and reduces the amount of information to encode
+in the angle vector. Encoding these vectors independently with
+residue backend #0 or residue backend #1 will result in bitrate
+savings. However, there are still implicit correlations between the
+magnitude and angle vectors. The most obvious is that the amplitude
+of the angle is bounded by its corresponding magnitude value.</p>
+
+<p>Entropy coding the results, then, further benefits from the entropy
+model being able to compress magnitude and angle simultaneously. For
+this reason, Vorbis implements residue backend #2 which pre-interleaves
+a number of input vectors (in the stereo case, two, A and B) into a
+single output vector (with the elements in the order of
+A_0, B_0, A_1, B_1, A_2 ... A_n-1, B_n-1) before entropy encoding. Thus
+each vector to be coded by the vector quantization backend consists of
+matching magnitude and angle values.</p>
+
+<p>The astute reader, at this point, will notice that in the theoretical
+case in which we can use monolithic codebooks of arbitrarily large
+size, we can directly interleave and encode left and right without
+polar mapping; in fact, the polar mapping does not appear to lend any
+benefit whatsoever to the efficiency of the entropy coding. In fact,
+it is perfectly possible and reasonable to build a Vorbis encoder that
+dispenses with polar mapping entirely and merely interleaves the
+channel. Libvorbis based encoders may configure such an encoding and
+it will work as intended.</p>
+
+<p>However, when we leave the ideal/theoretical domain, we notice that
+polar mapping does give additional practical benefits, as discussed in
+the above section on polar mapping and summarized again here:</p>
+
+<ul>
+<li>Polar mapping aids in controlling entropy 'leakage' between stages
+of a cascaded codebook.</li>
+<li>Polar mapping separates the stereo image
+into point and diffuse components which may be analyzed and handled
+differently.</li>
+</ul>
+
+<h2>Stereo Models</h2>
+
+<h3>Dual Stereo</h3>
+
+<p>Dual stereo refers to stereo encoding where the channels are entirely
+separate; they are analyzed and encoded as entirely distinct entities.
+This terminology is familiar from mp3.</p>
+
+<h3>Lossless Stereo</h3>
+
+<p>Using polar mapping and/or channel interleaving, it's possible to
+couple Vorbis channels losslessly, that is, construct a stereo
+coupling encoding that both saves space but also decodes
+bit-identically to dual stereo. OggEnc 1.0 and later uses this
+mode in all high-bitrate encoding.</p>
+
+<p>Overall, this stereo mode is overkill; however, it offers a safe
+alternative to users concerned about the slightest possible
+degradation to the stereo image or archival quality audio.</p>
+
+<h3>Phase Stereo</h3>
+
+<p>Phase stereo is the least aggressive means of gracefully dropping
+resolution from the stereo image; it affects only diffuse imaging.</p>
+
+<p>It's often quoted that the human ear is deaf to signal phase above
+about 4kHz; this is nearly true and a passable rule of thumb, but it
+can be demonstrated that even an average user can tell the difference
+between high frequency in-phase and out-of-phase noise. Obviously
+then, the statement is not entirely true. However, it's also the case
+that one must resort to nearly such an extreme demonstration before
+finding the counterexample.</p>
+
+<p>'Phase stereo' is simply a more aggressive quantization of the polar
+angle vector; above 4kHz it's generally quite safe to quantize noise
+and noisy elements to only a handful of allowed phases, or to thin the
+phase with respect to the magnitude. The phases of high amplitude
+pure tones may or may not be preserved more carefully (they are
+relatively rare and L/R tend to be in phase, so there is generally
+little reason not to spend a few more bits on them)</p>
+
+<h4>example: eight phase stereo</h4>
+
+<p>Vorbis may implement phase stereo coupling by preserving the entirety
+of the magnitude vector (essential to fine amplitude and energy
+resolution overall) and quantizing the angle vector to one of only
+four possible values. Given that the magnitude vector may be positive
+or negative, this results in left and right phase having eight
+possible permutation, thus 'eight phase stereo':</p>
+
+<p><img src="eightphase.png" alt="eight phase"/></p>
+
+<p>Left and right may be in phase (positive or negative), the most common
+case by far, or out of phase by 90 or 180 degrees.</p>
+
+<h4>example: four phase stereo</h4>
+
+<p>Similarly, four phase stereo takes the quantization one step further;
+it allows only in-phase and 180 degree out-out-phase signals:</p>
+
+<p><img src="fourphase.png" alt="four phase"/></p>
+
+<h3>example: point stereo</h3>
+
+<p>Point stereo eliminates the possibility of out-of-phase signal
+entirely. Any diffuse quality to a sound source tends to collapse
+inward to a point somewhere within the stereo image. A practical
+example would be balanced reverberations within a large, live space;
+normally the sound is diffuse and soft, giving a sonic impression of
+volume. In point-stereo, the reverberations would still exist, but
+sound fairly firmly centered within the image (assuming the
+reverberation was centered overall; if the reverberation is stronger
+to the left, then the point of localization in point stereo would be
+to the left). This effect is most noticeable at low and mid
+frequencies and using headphones (which grant perfect stereo
+separation). Point stereo is is a graceful but generally easy to
+detect degradation to the sound quality and is thus used in frequency
+ranges where it is least noticeable.</p>
+
+<h3>Mixed Stereo</h3>
+
+<p>Mixed stereo is the simultaneous use of more than one of the above
+stereo encoding models, generally using more aggressive modes in
+higher frequencies, lower amplitudes or 'nearly' in-phase sound.</p>
+
+<p>It is also the case that near-DC frequencies should be encoded using
+lossless coupling to avoid frame blocking artifacts.</p>
+
+<h3>Vorbis Stereo Modes</h3>
+
+<p>Vorbis, as of 1.0, uses lossless stereo and a number of mixed modes
+constructed out of lossless and point stereo. Phase stereo was used
+in the rc2 encoder, but is not currently used for simplicity's sake. It
+will likely be re-added to the stereo model in the future.</p>
+
+<div id="copyright">
+ The Xiph Fish Logo is a
+ trademark (™) of Xiph.Org.<br/>
+
+ These pages © 1994 - 2005 Xiph.Org. All rights reserved.
+</div>
+
+</body>
+</html>
+
+
+
+
+
+
projects / platform / upstream / libvorbis.git / blobdiff