 Matrix decoder

Matrix decoder is an audio technology where a finite number of discrete audio channels (e.g., 2) are decoded into a larger number of channels on play back (e.g., 5). The channels are generally, but not always, arranged for transmission or recording by an encoder, and decoded for playback by a decoder.
The function is to allow multichannel audio, such as quadraphonic sound or surround sound to be encoded in a stereo signal, and thus played back as stereo on stereo equipment, and as surround on surround equipment – this is "compatible" multichannel audio.
Process
Matrix encoding does not allow one to encode several channels in fewer channels without losing information: one cannot fit 5 channels into 2 (or even 3 into 2) without losing information, as this loses dimensions: the decoded signals are not independent. The idea is rather to encode something that will both be an acceptable approximation of the surround sound when decoded, and acceptable (or even superior) stereo.
Notation
The notation for matrix encoding consists of the number of discrete audio channels separated by a colon from the number of decoded channels. For example, two discrete channels decoded to fourchannels would be notated:
2:4
Five discrete channels decoded to six channels would be notated:
5:6
Many matrix decoders take advantage of the Haas effect^{[citation needed]}, as well as audio cues inherent in the source channels.
The various encoding matrixes are described below.
SQ matrix encoding (2:4, "Stereo Quadraphonic", CBS SQ)
Encoding matrix Left Front Right Front Left Back Right Back Left Total 1.0 0.0 k0.7 0.7 Right Total 0.0 1.0 0.7 j0.7 phaseshift, phaseshift
This above is the basic "4/2" (4 channels in, 2 out) encoding equation and after 1972, wasn't much used by CBS and others... The basic SQ 4/2 code had mono/stereo anomalies as well as encoding/decoding problems  these were heavily criticized by Michael Gerzon and others, so CBS corrected them all with the SQ Position Encoder, the ForwardOriented Encoder, the BackwardsOriented Encoder and the "London Box."
Position Encoder: An N/2 encoder that encoded every position in a 360° circle  it had 16 inputs and each could be dialed to the exact direction desired, generating an optimized encode.
ForwardOriented encoder:
Encoding matrix Left Front Right Front Left Back Right Back Left Total 1.0 0.0 0.7 k0.7 Right Total 0.0 1.0 k0.7 0.7 phaseshift, phaseshift
ForwardOriented encoder: Caused Center Back to be encoded as Center Front and was recommended for live broadcast use for maximum mono compatibility  it also encoded Center Left/Center Right and both diagonal splits in the optimal manner. Could be used to modify existing 2channel stereo recordings and create 'synthesized SQ' that when played through a FullLogic or Tate DES SQ decoder, exhibited a 180° or 270° synthesized quad effect. Many stereo FM radio stations broadcasting SQ in the 70's used their ForwardOriented SQ encoder for this. For SQ decoders, CBS designed a circuit that produced the 270° enhancement using the 90° phase shifters in the decoder. Sansui's QS Encoders and QS VarioMatrix Decoders had a similar capability.
BackwardsOriented encoder:
Encoding matrix Left Front Right Front Left Back Right Back Left Total 1.0 0.0 k0.7 0.7 Right Total 0.0 1.0 0.7 j0.7 phaseshift, phaseshift
BackwardsOriented Encoder: Was the reverse of the ForwardOriented Encoder  it allowed sounds to be placed optimally in the back half of the room, but monocompatibility was sacrificed. When used with standard stereo recordings it created "extra wide" stereo with sounds outside the speakers.
Some encoding mixers had channel strips switchable between forwardoriented and backwardsoriented encodong.
London Box: Encoded Center Back in such a way that it didn't cancel in mono playback, thus its output was usually mixed with that of a Position Encoder or a Forward Oriented encoder. After 1972, the vast majority of SQ Encoded albums were mixed with either the Position Encoder or the ForwardOriented encoder.
In addition, CBS created the SQ Ghent Microphone, which was a spatial microphone system using the Neumann QM69 mic. The signals from the QM69 were differenced, and then phasematrixed into 2channel SQ.^{[1]} With the Ghent Microphone, SQ was transformed from a Matrix into a Kernel and an additional signal could be derived to provide N:3:4 performance.
In 1976, Ben Bauer integrated matrix and discrete systems into USQ, or Universal SQ. (others had done this with their quad systems too) It was a hierarchical 444 discrete matrix that used the SQ matrix as the baseband for discrete quadraphonic FM broadcasts using additional difference signals called "T" and "Q". For a USQ FM broadcast, the additional "T" modulation was placed at 38kHz in quadrature to the standard stereo difference signal and the "Q" modulation was placed on a carrier at 76kHz. For standard 2channel SQ Matrix broadcasts, CBS recommended that an optional pilottone be placed at 19kHz in quadrature to the regular pilottone to indicate SQ encoded signals and activate the listeners Logic decoder. CBS argued that the SQ system should be selected as the standard for quadraphonic FM because, in FCC listening tests of the various four channel broadcast proposals, the 4:2:4 SQ system, decoded with a CBS Paramatrix decoder, outperformed 4:3:4 (without logic) as well as all other 4:2:4 (with logic) systems tested, approaching the performance of a discrete master tape within a very slight margin.^{[2]} At the same time, the SQ "fold" to stereo and mono was preferred to the stereo and mono "fold" of 4:4:4, 4:3:4 and all other 4:2:4 encoding systems.
The Directional Enhancement System, also known as the Tate DES, was an advanced decoder for SQ (although it could be made to work with any matrix or kernel system) and enhanced the directionality of the basic SQ matrix. It first matrixed the four outputs of the SQ decoder to derive additional signals, then compared their envelopes to detect the predominant direction and degree of dominance. A processor section, implemented outside of the Tate IC chips, applied variable attack/decay timing to the control signals and determined the coefficients of the "B" (Blend) matrices needed to enhance the directionality. These were acted upon by true analog multipliers in the Matrix Multiplier IC's, to multiply the incoming matrix by the "B" matrices and produce outputs in which the directionality of all predominant sounds were enhanced. Since the DES could recognize all three directions of the Energy Sphere simultaneously, and enhance the separation, it had a very open and 'discrete' sounding soundfield. In addition, the enhancement was done with sufficient additional complexity that all nondominant sounds were kept at their proper levels. Dolby used the Tate DES IC's in their theater processors until around 1986, when they developed the Pro Logic system. Unfortunately, delays and problems kept the Tate DES IC's from the market until the late 70's and only two consumer decoders were ever made that employed them, the Audionics Space & Image Composer and the Fosgate Tate II 101A. The Fosgate used a faster, updated version of the IC, called the Tate II, and additional circuitry that provided for separation enhancement around the full 360 soundfield. Unlike the earlier Full Wavematching Logic decoders for SQ, that varied the output levels to enhance directionality, the Tate DES cancelled SQ signal crosstalk as a function of the predominant directionality, keeping nondominant sounds and reverberation in its proper spatial locations at at their correct level.
QS matrix encoding (2:4, "Quadraphonic Sound", QS)
Encoding matrix Left Front Right Front Left Back Right Back Left Total 0.92 0.38 j0.92 j0.38 Right Total 0.38 0.92 k0.38 k0.92 phaseshift, phaseshift
Ambisonic UHJ kernel encoding (2:3)
Encoding matrix W (pressure signal) X (frontback signal) Y (leftright signal) Left Total 0.470 + k0.171 0.093 + j0.255 +0.328 Right Total 0.470 + j0.171 0.093 + k0.255 0.328 phaseshift, phaseshift
For more details on this topic, see Ambisonic UHJ format.Dolby MP matrix encoding (2:4)
^{[dubious – discuss]}
Encoding matrix Left Right Center Surround Left Total 1 0 Right Total 0 1 phaseshift, phaseshift
Note, Dolby MP Matrix is the name of the 4:2:4 encoding matrix. The term "Dolby Surround" refers to both the encoding and decoding in the home environment, while in the theater it is known Dolby Stereo.
Dolby Pro Logic matrix (2:4)
^{[dubious – discuss]}
Encoding matrix Left Right Center Surround Left Total 1 0 Right Total 0 1 phaseshift, phaseshift
The encoding matrix is the same as for Dolby Surround; only the Pro Logic decoder differs. There is no such thing as a Pro Logic encoder.
Dolby Pro Logic II matrix encoding (2:5)
Encoding matrix Left Right Center Rear Left Rear Right Left Total 1 0 Right Total 0 1 phaseshift, phaseshift
References
 ^ Bauer, Benjamin B.; Louis A. Abbagnaro, Daniel W. Gravereaux, and Trevor J. Marshall (January/February 1978). "The Ghent Microphone System for SQ Quadraphonic Recording and Broadcasting". Journal of the Audio Engineeriong Society (AES) 26 (Number 1/2): pp. 2–11.
 ^ “A subjective evaluation of FM Quadraphonic reproduction systems – Listening tests” Federal Communications Commission, Office of the Chief Engineer, Laboratory Division, Laurel, Maryland. Project Number 27101, August 1977
See also
Categories: Sound
 Technology stubs
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