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Matrix decoding is an audio technology where a small 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.

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.

The earliest and simpler form of decoding is the Hafler circuit, deriving back channels out of normal stereo recording (2:2:4). It was used for decoding only (encoding sound was not considered).

Decoding matrix Left Front Right Front Left Back Right Back Left Total 1.0 0.0 1.0 1.0 Right Total 0.0 1.0 1.0 1.0

The Dynaquad matrix introduced in 1969 was based on the Hafler circuit, but also used for a specific encoding of 4 sound channels in some albums (4:2:4).

Matrix Left Front Right Front Left Back Right Back Left Total 1.0 0.25 1.0 0.5 Right Total 0.25 1.0 0.5 1.0

Matrix Left Front Right Front Left Back Right Back Left Total 1.0 0.0 0.64 0.36 Right Total 0.0 1.0 0.36 0.64

The Stereo 4 matrix was invented by Leonard Feldman and Jon Fixler, introduced in 1970, and sold by Electro Voice and Radio Shack. This matrix was used to encode 4 sound channels on many record albums (4:2:4).

Matrix Left Front Right Front Left Back Right Back Left Total 1.0 0.3 1.0 0.5 Right Total 0.3 1.0 0.5 1.0

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.

It encoded the 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 Forward Oriented encoder.

In addition, CBS created the SQ Ghent Microphone, which was a spatial microphone system using the Neumann QM 69 mic. The signals from the QM 69 were differenced, and then phase matrixed into 2 channel SQ. 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. It was a hierarchical 4 4 4 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 38 kHz in quadrature to the standard stereo difference signal and the "Q" modulation was placed on a carrier at 76 kHz. For standard 2 channel SQ Matrix broadcasts, CBS recommended that an optional pilot tone be placed at 19 kHz in quadrature to the regular pilot tone 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. 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 that 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 non dominant 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 1970s 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 Wave matching 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 non dominant sounds and reverberation in its proper spatial locations at their correct level.