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| author | Aki <please@ignore.pl> | 2021-09-29 22:52:49 +0200 |
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| committer | Aki <please@ignore.pl> | 2021-09-29 22:52:49 +0200 |
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diff --git a/doc/stereo.html b/doc/stereo.html new file mode 100644 index 0000000..9cfbbea --- /dev/null +++ b/doc/stereo.html @@ -0,0 +1,419 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html> +<head> + +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-15"/> +<title>Ogg Vorbis Documentation</title> + +<style type="text/css"> +body { + margin: 0 18px 0 18px; + padding-bottom: 30px; + font-family: Verdana, Arial, Helvetica, sans-serif; + color: #333333; + font-size: .8em; +} + +a { + color: #3366cc; +} + +img { + border: 0; +} + +#xiphlogo { + margin: 30px 0 16px 0; +} + +#content p { + line-height: 1.4; +} + +h1, h1 a, h2, h2 a, h3, h3 a, h4, h4 a { + font-weight: bold; + color: #ff9900; + margin: 1.3em 0 8px 0; +} + +h1 { + font-size: 1.3em; +} + +h2 { + font-size: 1.2em; +} + +h3 { + font-size: 1.1em; +} + +li { + line-height: 1.4; +} + +#copyright { + margin-top: 30px; + line-height: 1.5em; + text-align: center; + font-size: .8em; + color: #888888; + clear: both; +} +</style> + +</head> + +<body> + +<div id="xiphlogo"> + <a href="http://www.xiph.org/"><img src="fish_xiph_org.png" alt="Fish Logo and Xiph.Org"/></a> +</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> + + + + + + |