M. A. Gerzon - SQ Matrix Problems

[kfbkfb]

__ (michaelgerzonphotos.org.uk)
^^^
...describes the permanent limitations producers will be subject to if the "SQ" system is adopted...


I found this again, thought it would be useful here.


Kirk Bayne

 

[Soundfield]

For those that don't know, that paper is accessible from Michael Gerzon’s biographical archive site. It can be found in the section on “Commercial Quadraphony” which, importantly, explains how it came to be written (in the context of the infamous CBS SQ demonstration in London)-
Commercial Quadraphonics
The paper should be read together with his broader analysis of the SQ system-
Anomalies in the CBS SQ system

Actually, the whole archive is fascinating, and well worth a visit if you haven’t already.

 

[Doug G.]

Yes but, does he hate SQ?

Interesting that he claims none of the phasor or QS type systems have any of the faults of SQ but then proceeds to call out faults of their own (e.g. poorer mono compatibility).

The thrust is that ALL matrix systems are a compromise. There really is no practical way they can't be.

Doug

 

[Soundfield]

Yes but, does he hate SQ?

Interesting that he claims none of the phasor or QS type systems have any of the faults of SQ but then proceeds to call out faults of their own (e.g. poorer mono compatibility).

The thrust is that ALL matrix systems are a compromise. There really is no practical way they can't be.

Doug

Yes, and that was exactly his point. He didn't 'hate' any system. He was an independent mathematician who pointed out the fundamental flaws in the SQ system in that particular paper (and was entirely correct). But he'd studied the shortcomings of all existing quad systems (including 'discrete') and felt there was a much better engineering solution, and was why he was trying to develop tetrahedral recording and the ambisonic system. You'll see, if you read the archive material, that he was so busy (and sick) that he did not have time to get around to a publishing a detailed critical analysis of the QS system before he died.

 

[MidiMagic]

I analyzed his papers and most of his objections to the SQ system were based on the 4-corners encoder equations that was the basis of the early SQ releases.

In the meantime CBS labs developed several encoder variations that overcome the objections in the papers:

- The original 4-corners encpoder was intended to convert discrete recordings to SQ.
- The acroperiphonic encoder puts a psi phase difference between the front channels and the back channels, allowing sounds to be encoded like they were overhead.
- The diagonal-split encoder concentrated on encoding sounds on opposite speakers.
- The front-oriented encoder encoded to the front and both sides in perfect phase.
- The back-oriented encoder encoded to the back and both sides in perfect phase.

All 5 of these can be put on the same 10-bus mixer. Any sound from the original 16 or 32 track multitrack tape can be routed to any of the encoders independently of any other sound. Then all 5 encoders are mixed together to make the SQ encoded master.

Only 3 matrix systems avoid cancellation of back sounds in mono play: BMX (and UD4), H, and Ambisonic.

 

[kfbkfb]

Recording-1973-12-OCR-Page-0024.pdf (worldradiohistory.com)
^^^
SQ encoding has been presented with a number of schemes...


IIRC, the 4212 SQ Position Encoder provides more channel separation on the diagonals than the original 4 input 4200 SQ Encoder.


Kirk Bayne

 

[stevendive]

Interesting that he claims none of the phasor or QS type systems have any of the faults of SQ but then proceeds to call out faults of their own (e.g. poorer mono compatibility).

The thrust is that ALL matrix systems are a compromise. There really is no practical way they can't be.

Doug
[/QUOTE]

Certainly any 2 channel limited matrixing is compromised unavoidably this way. The omlett can only be unscrambled to a limited extent, which In UHJ (BHJ) is by de-matrixing the 2 channels to 3 in decoders. Two and a half & three and 4 channel UHJ (SHJ, THJ & PHJ), which never were to become known in actual use, remove the direction related phase error by including the error signal in the 2.5 (band limited - SHJ) or third channel full range (THJ) so it could be combined in the ambi decoder to fully reproduce the unmatrixed B-Format (horizontal) signals that then goes via the shelf filters to the amplitude matrix that produces the loudspeaker feeds. Full B-Format itself is not compromised by channel number limitation.

https://stason.org/TULARC/entertainment/audio/ambisonic/8-What-are-BHJ-SHJ-THJ-and-PHJ.html
https://en.wikipedia.org/wiki/Ambisonic_UHJ_format
Regarding the sometimes misunderstood shelf filters, it is worth pointing out that ambisonic decoders are divided into both velocity and energy optimised decoding bands at these filters, they do not remove energy overall. For 1st order ambi decoders, this division at the filters is into rV (LF <200 Hz) and rE (>800 Hz) sections, is arranged to ensure the cues from both are never in conflict at any point. The frequency band division in the decoder is designed to take into account two things, 1 - the progressive breakdown of smooth refraction around the head as frequency rises, and our hearning perception switching rapidly to energy difference between the ears over this range, and 2 - the reducing accuracy of the wave pattern reconstruction area itself as frequency rises. The accurate velocity reconstruction wave pattern is about one full wavelength for 1st order, 2 wavelengths at 2nd order, etc.

Gerzon's work and metatheory laid the foundations for HOA, currently used in VR but could be used for home listening over loudspeakers, up to maybe 8 horizontal for 3rd order practically, and is used currently in some sound installations (eg. for audio research and demos).