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77 <p>The Vorbis audio CODEC provides a channel coupling
78 mechanisms designed to reduce effective bitrate by both eliminating
79 interchannel redundancy and eliminating stereo image information
80 labeled inaudible or undesirable according to spatial psychoacoustic
81 models. This document describes both the mechanical coupling
82 mechanisms available within the Vorbis specification, as well as the
83 specific stereo coupling models used by the reference
89 channel encoding, but the channels were encoded entirely separately
90 with no cross-analysis or redundancy elimination between channels.
91 This multichannel strategy is very similar to the mp3's <em>dual
92 stereo</em> mode and Vorbis uses the same name for its analogous
93 uncoupled multichannel modes.</p>
96 later implement a coupled channel strategy. Vorbis has two specific
97 mechanisms that may be used alone or in conjunction to implement
100 mapping</em>. These two general mechanisms are particularly well
101 suited to coupling due to the structure of Vorbis encoding, as we'll
102 explore below, and using both we can implement both totally
104 to uncoupled modes], as well as various lossy models that seek to
105 eliminate inaudible or unimportant aspects of the stereo image in
106 order to enhance bitrate. The exact coupling implementation is
107 generalized to allow the encoder a great deal of flexibility in
108 implementation of a stereo or surround model without requiring any
109 significant complexity increase over the combinatorially simpler
110 mid/side joint stereo of mp3 and other current audio codecs.</p>
112 <p>A particular Vorbis bitstream may apply channel coupling directly to
113 more than a pair of channels; polar mapping is hierarchical such that
114 polar coupling may be extrapolated to an arbitrary number of channels
115 and is not restricted to only stereo, quadraphonics, ambisonics or 5.1
116 surround. However, the scope of this document restricts itself to the
117 stereo coupling case.</p>
123 <p>Recall that the basic structure of a a Vorbis I stream first generates
124 from input audio a spectral 'floor' function that serves as an
125 MDCT-domain whitening filter. This floor is meant to represent the
126 rough envelope of the frequency spectrum, using whatever metric the
127 encoder cares to define. This floor is subtracted from the log
128 frequency spectrum, effectively normalizing the spectrum by frequency.
129 Each input channel is associated with a unique floor function.</p>
131 <p>The basic idea behind any stereo coupling is that the left and right
132 channels usually correlate. This correlation is even stronger if one
133 first accounts for energy differences in any given frequency band
134 across left and right; think for example of individual instruments
135 mixed into different portions of the stereo image, or a stereo
136 recording with a dominant feature not perfectly in the center. The
137 floor functions, each specific to a channel, provide the perfect means
138 of normalizing left and right energies across the spectrum to maximize
139 correlation before coupling. This feature of the Vorbis format is not
140 a convenient accident.</p>
142 <p>Because we strive to maximally correlate the left and right channels
143 and generally succeed in doing so, left and right residue is typically
144 nearly identical. We could use channel interleaving (discussed below)
145 alone to efficiently remove the redundancy between the left and right
146 channels as a side effect of entropy encoding, but a polar
147 representation gives benefits when left/right correlation is
148 strong.</p>
152 <p>The first advantage of a polar representation is that it effectively
153 separates the spatial audio information into a 'point image'
154 (magnitude) at a given frequency and located somewhere in the sound
155 field, and a 'diffuse image' (angle) that fills a large amount of
156 space simultaneously. Even if we preserve only the magnitude (point)
157 data, a detailed and carefully chosen floor function in each channel
158 provides us with a free, fine-grained, frequency relative intensity
159 stereo*. Angle information represents diffuse sound fields, such as
160 reverberation that fills the entire space simultaneously.</p>
163 stereo models and these models may be mixed, we do not use the term
164 'intensity stereo' talking about Vorbis; instead we use the terms
165 'point stereo', 'phase stereo' and subcategories of each.</em></p>
167 <p>The majority of a stereo image is representable by polar magnitude
168 alone, as strong sounds tend to be produced at near-point sources;
169 even non-diffuse, fast, sharp echoes track very accurately using
170 magnitude representation almost alone (for those experimenting with
171 Vorbis tuning, this strategy works much better with the precise,
173 results in unstable imaging). Reverberation and diffuse sounds tend
174 to contain less energy and be psychoacoustically dominated by the
175 point sources embedded in them. Thus, we again tend to concentrate
176 more represented energy into a predictably smaller number of numbers.
177 Separating representation of point and diffuse imaging also allows us
178 to model and manipulate point and diffuse qualities separately.</p>
182 <p>Because polar
183 representation concentrates represented energy into fewer large
184 values, we reduce bit 'leakage' during cascading (multistage VQ
185 encoding) as a secondary benefit. A single large, monolithic VQ
186 codebook is more efficient than a cascaded book due to entropy
187 'crosstalk' among symbols between different stages of a multistage cascade.
188 Polar representation is a way of further concentrating entropy into
189 predictable locations so that codebook design can take steps to
190 improve multistage codebook efficiency. It also allows us to cascade
191 various elements of the stereo image independently.</p>
195 <p>Rounding and computational complexity are potential problems with a
196 polar representation. As our encoding process involves quantization,
197 mixing a polar representation and quantization makes it potentially
198 impossible, depending on implementation, to construct a coupled stereo
199 mechanism that results in bit-identical decompressed output compared
200 to an uncoupled encoding should the encoder desire it.</p>
202 <p>Vorbis uses a mapping that preserves the most useful qualities of
203 polar representation, relies only on addition/subtraction (during
204 decode; high quality encoding still requires some trig), and makes it
205 trivial before or after quantization to represent an angle/magnitude
206 through a one-to-one mapping from possible left/right value
207 permutations. We do this by basing our polar representation on the
208 unit square rather than the unit-circle.</p>
210 <p>Given a magnitude and angle, we recover left and right using the
211 following function (note that A/B may be left/right or right/left
212 depending on the coupling definition used by the encoder):</p>
214 <pre>
217 A=magnitude;
218 B=magnitude-angle;
219 }else{
220 B=magnitude;
221 A=magnitude+angle;
222 }
223 else
225 A=magnitude;
226 B=magnitude+angle;
227 }else{
228 B=magnitude;
229 A=magnitude-angle;
230 }
231 }
232 </pre>
234 <p>The function is antisymmetric for positive and negative magnitudes in
235 order to eliminate a redundant value when quantizing. For example, if
236 we're quantizing to integer values, we can visualize a magnitude of 5
241 <p>This representation loses or replicates no values; if the range of A
243 permutations is 121. Represented in square polar notation, the
244 possible values are:</p>
246 <pre>
259 </pre>
265 It's also obvious that this mapping is exactly reversible.</p>
269 <p>We can remap and A/B vector using polar mapping into a magnitude/angle
270 vector, and it's clear that, in general, this concentrates energy in
271 the magnitude vector and reduces the amount of information to encode
272 in the angle vector. Encoding these vectors independently with
274 savings. However, there are still implicit correlations between the
275 magnitude and angle vectors. The most obvious is that the amplitude
276 of the angle is bounded by its corresponding magnitude value.</p>
278 <p>Entropy coding the results, then, further benefits from the entropy
279 model being able to compress magnitude and angle simultaneously. For
280 this reason, Vorbis implements residue backend #2 which pre-interleaves
281 a number of input vectors (in the stereo case, two, A and B) into a
282 single output vector (with the elements in the order of
284 each vector to be coded by the vector quantization backend consists of
285 matching magnitude and angle values.</p>
287 <p>The astute reader, at this point, will notice that in the theoretical
288 case in which we can use monolithic codebooks of arbitrarily large
289 size, we can directly interleave and encode left and right without
290 polar mapping; in fact, the polar mapping does not appear to lend any
291 benefit whatsoever to the efficiency of the entropy coding. In fact,
292 it is perfectly possible and reasonable to build a Vorbis encoder that
293 dispenses with polar mapping entirely and merely interleaves the
294 channel. Libvorbis based encoders may configure such an encoding and
295 it will work as intended.</p>
297 <p>However, when we leave the ideal/theoretical domain, we notice that
298 polar mapping does give additional practical benefits, as discussed in
299 the above section on polar mapping and summarized again here:</p>
301 <ul>
302 <li>Polar mapping aids in controlling entropy 'leakage' between stages
303 of a cascaded codebook.</li>
304 <li>Polar mapping separates the stereo image
305 into point and diffuse components which may be analyzed and handled
306 differently.</li>
307 </ul>
313 <p>Dual stereo refers to stereo encoding where the channels are entirely
314 separate; they are analyzed and encoded as entirely distinct entities.
315 This terminology is familiar from mp3.</p>
319 <p>Using polar mapping and/or channel interleaving, it's possible to
320 couple Vorbis channels losslessly, that is, construct a stereo
321 coupling encoding that both saves space but also decodes
322 bit-identically to dual stereo. OggEnc 1.0 and later uses this
323 mode in all high-bitrate encoding.</p>
325 <p>Overall, this stereo mode is overkill; however, it offers a safe
326 alternative to users concerned about the slightest possible
327 degradation to the stereo image or archival quality audio.</p>
331 <p>Phase stereo is the least aggressive means of gracefully dropping
332 resolution from the stereo image; it affects only diffuse imaging.</p>
334 <p>It's often quoted that the human ear is deaf to signal phase above
335 about 4kHz; this is nearly true and a passable rule of thumb, but it
336 can be demonstrated that even an average user can tell the difference
337 between high frequency in-phase and out-of-phase noise. Obviously
338 then, the statement is not entirely true. However, it's also the case
339 that one must resort to nearly such an extreme demonstration before
340 finding the counterexample.</p>
342 <p>'Phase stereo' is simply a more aggressive quantization of the polar
343 angle vector; above 4kHz it's generally quite safe to quantize noise
344 and noisy elements to only a handful of allowed phases, or to thin the
345 phase with respect to the magnitude. The phases of high amplitude
346 pure tones may or may not be preserved more carefully (they are
347 relatively rare and L/R tend to be in phase, so there is generally
348 little reason not to spend a few more bits on them)</p>
352 <p>Vorbis may implement phase stereo coupling by preserving the entirety
353 of the magnitude vector (essential to fine amplitude and energy
354 resolution overall) and quantizing the angle vector to one of only
355 four possible values. Given that the magnitude vector may be positive
356 or negative, this results in left and right phase having eight
357 possible permutation, thus 'eight phase stereo':</p>
361 <p>Left and right may be in phase (positive or negative), the most common
366 <p>Similarly, four phase stereo takes the quantization one step further;
373 <p>Point stereo eliminates the possibility of out-of-phase signal
374 entirely. Any diffuse quality to a sound source tends to collapse
375 inward to a point somewhere within the stereo image. A practical
376 example would be balanced reverberations within a large, live space;
377 normally the sound is diffuse and soft, giving a sonic impression of
378 volume. In point-stereo, the reverberations would still exist, but
379 sound fairly firmly centered within the image (assuming the
380 reverberation was centered overall; if the reverberation is stronger
381 to the left, then the point of localization in point stereo would be
382 to the left). This effect is most noticeable at low and mid
383 frequencies and using headphones (which grant perfect stereo
384 separation). Point stereo is is a graceful but generally easy to
385 detect degradation to the sound quality and is thus used in frequency
386 ranges where it is least noticeable.</p>
390 <p>Mixed stereo is the simultaneous use of more than one of the above
391 stereo encoding models, generally using more aggressive modes in
392 higher frequencies, lower amplitudes or 'nearly' in-phase sound.</p>
394 <p>It is also the case that near-DC frequencies should be encoded using
395 lossless coupling to avoid frame blocking artifacts.</p>
400 constructed out of lossless and point stereo. Phase stereo was used
401 in the rc2 encoder, but is not currently used for simplicity's sake. It
402 will likely be re-added to the stereo model in the future.</p>
405 The Xiph Fish Logo is a
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