Editing Matrix decoder (section)

== SQ matrix, "Stereo Quadraphonic", CBS SQ (4:2:4) ==
{{Main|Stereo Quadraphonic}}
{| class="wikitable"
|-
! 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
|}
''<math>j = +90^\circ</math> phase-shift, <math>k = -90^\circ</math> phase-shift''

The basic SQ matrix had mono/stereo anomalies as well as encoding/decoding problems, heavily criticized by [[Michael Gerzon]] and others.<ref name="NewScientist">{{cite magazine |last1=Gerzon |first1=Michael |author-link1=Michael Gerzon |date=8 December 1977 |title=Don't say quad&mdash;say psychoacoustics |journal=New Scientist |pages=634–636 |quote=The forward oriented encoder is one of at least six different encoding options offered by SQ so that producers can decide for themselves which collection of faults they prefer.}}</ref>

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

=== 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.

=== Forward-Oriented encoder ===
{| class="wikitable"
|-
! 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
|}
''<math>j = +90^\circ</math> phase-shift, <math>k = -90^\circ</math> phase-shift''

The Forward-Oriented 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 2-channel stereo recordings and create 'synthesized SQ' that when played through a Full-Logic or Tate DES SQ decoder, exhibited a 180° or 270° synthesized quad effect. Many stereo FM radio stations broadcasting SQ in the 1970s used their Forward-Oriented 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 Electric|Sansui]]'s QS Encoders and QS Vario-Matrix Decoders had a similar capability.

=== Backwards-Oriented encoder ===
{| class="wikitable"
|-
! Matrix !! Left Front !! Right Front !! Left Back !! Right Back
|-
! Left Total 
| k1.0 || 0.0 || k0.7 || 0.7
|-
! Right Total 
| 0.0 || j1.0 || -0.7 || j0.7
|}
''<math>j = +90^\circ</math> phase-shift, <math>k = -90^\circ</math> phase-shift''

The Backwards-Oriented Encoder was the reverse of the Forward-Oriented Encoder - it allowed sounds to be placed optimally in the back half of the room, but mono-compatibility 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 forward-oriented and backwards-oriented encoding.

=== London Box ===
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.

=== Ghent microphone ===
In addition, CBS created the SQ Ghent Microphone, which was a spatial microphone system using the [[Georg Neumann|Neumann]] QM-69 mic. The signals from the QM-69 were differenced, and then phase-matrixed into 2-channel SQ.<ref>{{cite journal
| last = Bauer
| first = Benjamin B.
|author2=Louis A. Abbagnaro |author3=Daniel W. Gravereaux |author4=Trevor J. Marshall
 |date=January–February 1978
| title = The Ghent Microphone System for SQ Quadraphonic Recording and Broadcasting
| journal = Journal of the Audio Engineering Society
| volume = 26
| issue = 1/2
| pages =2–11
| publisher = [[Audio Engineering Society|AES]]
}}</ref>
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.

=== Universal SQ ===
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&nbsp;kHz in quadrature to the standard stereo difference signal and the "Q" modulation was placed on a carrier at 76&nbsp;kHz. For standard 2-channel SQ Matrix broadcasts, CBS recommended that an optional pilot-tone be placed at 19&nbsp;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.<ref>“A subjective evaluation of FM Quadraphonic reproduction systems – Listening tests” Federal Communications Commission, Office of the Chief Engineer, Laboratory Division, Laurel, Maryland. Project Number 2710-1, August 1977</ref> 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.

=== Tate DES decoder ===
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{{clarify|date=September 2022}} simultaneously, and enhance the separation, it had a very open and 'discrete'{{clarify|date=September 2022}} 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.