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.

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 original discrete audio channels separated by a colon from the number of encoded and decoded channels. For example, four channels encoded into two discrete channels and decoded back to four-channels would be notated:

4:2:4

Some methods derive new channels from the existing ones, with no special encoding of the audio source. For example, five discrete channels decoded to six channels would be notated:

5:5:6

Such derived channel "decoders" may take advantage of the Haas effect, as well as audio cues inherent in the source channels.

Many matrix encoding methods have been developed:

Hafler circuit (2:2:4)

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).

Dynaquad matrix (2:2:4) / (4:2:4)

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).^[1]

Electro-Voice Stereo-4 matrix (2:2:4) / (4:2:4)

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).^[3]

SQ matrix, "Stereo Quadraphonic", CBS SQ (4:2:4)

${\displaystyle j=+90^{\circ }}$ phase-shift, ${\displaystyle k=-90^{\circ }}$ phase-shift

The basic SQ matrix had mono/stereo anomalies as well as encoding/decoding problems, heavily criticized by Michael Gerzon and others.^[4]

An attempt to improve the system lead to the use of other encoders or sound capture techniques, yet the decoding matrix remained unchanged.

QS matrix, "Regular Matrix", "Quadraphonic Sound" (4:2:4)

${\displaystyle j=+90^{\circ }}$ phase-shift, ${\displaystyle k=-90^{\circ }}$ phase-shift

Matrix H (4:2:4)

j = 20° phase-shift k = 25° phase-shift l = 55° phase-shift m = 115° phase-shift

Ambisonic UHJ kernel (3:2:4 or more)

${\displaystyle j=+90^{\circ }}$ phase-shift, ${\displaystyle k=-90^{\circ }}$ phase-shift

Dolby Stereo and Dolby Surround (matrix) 4:2:4

Dolby Stereo and Dolby Surround are also known as Dolby MP, Dolby SVA and Pro Logic.

Dolby SVA matrix is the original name of the Dolby Stereo 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 Motion Picture matrix" or "Dolby MP". "Pro Logic" refers to the decoder used, there is no special Pro Logic encoding matrix.

The Ultra Stereo system, developed by different company, is compatible and uses similar matrixes to Dolby Stereo.

The Dolby Stereo Matrix is straightforward: the four original channels: Left (L), Center (C), Right (R), and Surround (S), are combined into two, known as Left-total (LT) and Right-total (RT) by this formula:

Dolby Stereo Mix	Left	Right	Center	Surround
Left Total	${\displaystyle 1}$	${\displaystyle 0}$	${\displaystyle {\frac {1}{\sqrt {2}}}}$	${\displaystyle +j{\frac {1}{\sqrt {2}}}}$
Right Total	${\displaystyle 0}$	${\displaystyle 1}$	${\displaystyle {\frac {1}{\sqrt {2}}}}$	${\displaystyle -j{\frac {1}{\sqrt {2}}}}$

where j = 90° phase-shift

The center channel information is carried by both LT and RT in phase, and surround channel information by both LT and RT but out of phase. The surround channel is a single limited frequency-range (7 kHz low-pass filtered^[8]) mono rear channel, dynamically compressed and placed with a lower volume than the rest. This allows for better separation of signals.

This gives good compatibility with both mono playback, which reproduces L, C and R from the mono speaker with C at a level 3 dB higher than L or R, but surround information cancels out. It also gives good compatibility with two-channel stereo playback where C is reproduced from both left and right speakers to form a phantom center and surround is reproduced from both speakers but in a diffuse manner.

A simple 4-channel decoder could simply send the sum signal (L+R) to the center speaker, and the difference signal (L-R) to the surrounds. But such a decoder would provide poor separation between adjacent speaker channels, thus anything intended for the center speaker would also reproduce from left and right speakers only 3 dB below the level in the center speaker. Similarly anything intended for the left speaker would be reproduced from both the center and surround speakers, again only 3 dB below the level in the left speaker. There is, however, complete separation between left and right, and between center and surround channels.

To overcome this problem the cinema decoder uses so-called "logic" circuitry to improve the separation. The logic circuitry decides which speaker channel has the highest signal level and gives it priority, attenuating the signals fed to the adjacent channels. Because there already is complete separation between opposite channels there is no need to attenuate those, in effect the decoder switches between L and R priority and C and S priority. This places some limitations on mixing for Dolby Stereo and to ensure that sound mixers mixed soundtracks appropriately they would monitor the sound mix via a Dolby Stereo encoder and decoder in tandem. In addition to the logic circuitry the surround channel is also fed via a delay, adjustable up to 100 ms to suit auditoria of differing sizes, to ensure that any leakage of program material intended for left or right speakers into the surround channel is always heard first from the intended speaker. This exploits the "Precedence effect" to localize the sound to the intended direction.

Dolby Pro Logic II matrix (5:2:5)

Matrix	Left	Right	Center	Rear Left	Rear Right
Left Total	${\displaystyle 1}$	${\displaystyle 0}$	${\displaystyle {\sqrt {\frac {1}{2}}}}$	${\displaystyle j{\frac {\sqrt {3}}{2}}}$	${\displaystyle j{\frac {1}{2}}}$
Right Total	${\displaystyle 0}$	${\displaystyle 1}$	${\displaystyle {\sqrt {\frac {1}{2}}}}$	${\displaystyle k{\frac {1}{2}}}$	${\displaystyle k{\frac {\sqrt {3}}{2}}}$

${\displaystyle j=+90^{\circ }}$ phase-shift, ${\displaystyle k=-90^{\circ }}$ phase-shift

The Pro Logic II matrix provides for stereo full frequency back channels. Normally a sub-woofer channel is driven by simply filtering and redirecting the existing bass frequencies of the original stereo track.

See also

• Ambisonic UHJ format
• Dolby Digital
• Dolby Pro Logic
• Haas effect
• Quadraphonic sound
• Surround sound

References