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.13.This has tobe done independently for different frequencies, i.e.for each subband or each criticalFigure 2.13 Main axis transform of the stereo plane (Reprinted from [Herre, 1995]© 1995, courtesy of the author)band.The idea has not been implemented in any real world audio coding systembecause more bits are spent to transmit the direction information than are gained bythis method.Two methods which have been used very successfully can be derived assimplifications of the main axis transform idea:M/S stereo coding simplifies on the original idea by reducing the number of possibledirections (to two).Intensity stereo coding does not reduce the number of directions but keeps only themain channel information for each subband.M/S stereo coding.M/S stereo coding was introduced to low bit-rate coding in[Johnston, 1989a].A matrixing operation similar to the technique used in FM stereotransmission is used in the coder with the appropriate dematrixing in the decoder: APPLICATIONS OF DSP TO AUDIO AND ACOUSTICS70Instead of transmitting the left and right signal, the normalized sum and differencesignals are handled (see Figure 2.14).They are referred to as the middle (M) and theFigure 2.14 Basic block diagram of M/S stereo coding (Reprinted from [Herre, 1995]© 1995, courtesy of the author)side (S) channel.The matrixing operation can be done in the time domain (i.e.beforethe analysis filter bank) as well as in the frequency domain (i.e.after the analysisfilter bank).Figure 2.15 shows the matrix operation.M/S stereo coding can be seenas a special case of a main axis transform of the input signal (see [van der Waal andVeldhuis, 1991]).Figure 2.15 Signal flow graph of the M/S matrix (Reprinted from [Herre, 1995] © 1995,courtesy of the author)The main features of M/S stereo processing can be described as follows [Herreet al., 1992]:Emphasis on redundancy removalThe main focus of M/S joint stereo coding is on the redundancy removal formono-like signals which often are critical for dual mono coding systems dueto the stereo unmasking effects described below.The maximum gain is thetheoretical gain of a main axis transform of a two-dimensional signal.However,stereo irrelevancy effects can be used in an M/S coding framework, too.Perfect reconstructionThe matrixing done in M/S joint stereo coding is invertible.Without the quanti-zation and coding of the matrix output the processing is completely transparent. PERCEPTUAL CODING OF HIGH QUALITY DIGITAL AUDIO 71Therefore M/S coding is applicable to higher bit-rate very high quality coding,too.Signal dependend bit-rate gainThe added coding efficiency of M/S stereo coding depends heavily on the actualsignal.It varies from a maximum of nearly 50% if the left and right channelsignals are equal (or exactly out of phase) to situations where M/S must not beused because of the possibility of new reverse unmasking effects.Useful for the whole spectral rangeBecause M/S matrixing basically preserves the full spatial information, it maybe applied to the full audio spectral range without the danger of the introductionof severe artifacts.Intensity stereo coding.Intensity stereo coding is another simplified approximationto the general idea of directional transform coding.For each subband which is trans-mitted using intensity stereo modes, just the intensity information is retained.Thedirectional information is transmitted via the coding of independent scalefactor valuesfor the left and right channels.Thus, only the energy envelope is transmitted for bothchannels.Due to the irrelevancy of exact location information at high frequencies thisFigure 2.16 Basic principle of intensity stereo coding (Reprinted from [Herre, 1995]© 1995, courtesy of the author)method is relatively successful.The main spatial cues are transmitted, however somedetails may be missing.It seems that this is especially obvious if the decoded signal isaudited using headphones (see [MPEG, 1991]).The main features of intensity stereo coding can be described as follows:Emphasis on irrelevancy reductionWhile signals with a large correlation of left versus right time domain signal stillbenefit from intensity stereo coding, the main emphasis is on the reduced spatialresolution at high frequencies. APPLICATIONS OF DSP TO AUDIO AND ACOUSTICS72Not perfect reconstructionThe signal components which are orthogonal in respect to the transmitted energymaximum are not transmitted, resulting in a loss of spatial information.Theenergy of the stereo signal is preserved, however.The potential loss of spatialinformation is considered to be less annoying than other coding artifacts.There-fore intensity stereo coding is mainly used at low bit-rates to prevent annoyingcoding artifacts.Saving of 50% of the sample dataFor the frequency range where intensity stereo coding is applied, only onechannel of subband data has to be transmitted.If we assume that intensity stereocoding is applied for half of the spectrum, we can assume a saving of about 20%of the net bit-rate.The maximum saving is at about 40%.Useful only for the high frequency rangeAs explained above, intensity stereo encoding is used only for part of the spec-trum.Extending intensity stereo processing towards low frequencies can causesevere artifacts such as a major loss of directional information.Coupling channels.In multichannel systems, a coupling channel is used as theequivalent to an n-channel intensity stereo system.This system is also known underthe names dynamic crosstalk or generalized intensity coding.Instead of n differentchannels, for part of the spectrum only one channel with added intensity information istransmitted.Coupling channels are used in AC-3 ([Fielder et al
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