Linear 2-->3 Rematrixing for Speaker Signals

[KSTR]

Note: Posts collected from "Beyond the Ariel" thread (I hope this is OK for everybody).

Originally posted by dobias
Gentlemen,
I don't recall seeing center speakers discussed in this (lengthly) thread.
I would like to spread out my OB speakers for furniture placement reasons. What are the pros & cons about using a center OB speaker?
If it is a reasonable addition, I remember(from my younger years)there were various ways to wire it, all with different disadvantages. Any wiring suggestions?
dobias

Originally posted by KSTR
Regarding driving of a three speaker setup which still is "normal stereo" in the preceived sound (actually it is usually quite better -- gives a more convincing illusion -- than 2-speaker-stereo), you might want to try what is known as "optimum linear matrix" and, in a more specific form, "trinaural". Properly set up, there are no**) disadvantages except that you need some time to get accustomed to the new and somewhat different soundfield represention -- kind of similar to effect of boomy bass one has gotten so used to until the first OB speaker was heard... now one knows what "boomy" really means, and after hearing OLM you will know what "scattered" means...

See Us.Pat.#5610986 (via http://pat2pdf.org), and the following websites:
http://www.milestech.com
http://www.ampzilla2000.com/trinaural.html

You need an additional line level hardware and three amplifiers. A purely passive approach at speaker signal levels using xformers might be possible, but will be quite hard to construct it as a really good working solution.

I don't know if there are any drawbacks from using OB speakers, but maybe there are -- at least there are asymmtrical (in time) reflections because the distance to front/rear wall is not the same for all three speakers.

EDIT: **) there are some disadvantages with recording tricks (HTRF based phantom localization way beyond the speaker baseline, laterally and, to a lesser extent, vertically) that rely on the use of the conventional stereo triangle, for example "Q-Sound"

- Klaus

Originally posted by dobias
Klaus,
Thank you very much for the information. As luck would have it, Mike Miles has his business a few hundred miles away here in Michigan.
I'll be in contact with him to work out the most inexpensive setup for me. I would like to have it work with my stereo amp but I'm willing to add an amp to have it work well.
It may be awhile before I can work it out but I'll let you know how it worked.
Do you have such an arrangement?
Frank

Originally posted by KSTR
Hi Frank,
Not in an actual simple working condition (ahem, the 3rd identical speaker that is needed). But I have tested it thoroughly (I also tested/measured one of the hardware devices available), working up on the theory (which has some roots way back in time, see the papers of A.D.Blumlein, and, more recently, M.Gerzon) and investigating many possible arrangements with a DAW-Software (digital audio workstation) and a multiple output soundcard (I have 24 channels, no lack of channels therefore ;-). The hardest part was, because of not having three identical speakers, trying to make them "equal" (small active monitors and a conventional passive floorstander) by use of allpass filters to correct for the different xovers and of course some EQing to get at least first order aproximations of identical responses. While severly compromised by the dissimilar speakers, these tests were nevertheless extremly promising, and quite a few people have tested "the real thing" with the processor (J.B.'s) and 3 identical full-ranging speakers (which really is very important, the typical home-cinema center is often not sufficent). Not everyone would find himself satisfied with the difference in the stereo representation, but those who did will most certainly never switch back. The stable soundstaging even with considerable head movement/turn and the overall increase in "spatial resolution" by a percieved order of magnitude is really stunning (@naysayers, this is not marketing bla-bla, I have no relationship with any company or any other interest other than to promote all this because im really convinced of it, in theory and in practise. It's a just another way of projecting stereo information into the room, another reproduction paradigm).

Currently, I'm saving money for a bigger overall system upgrade and might meanwhile try some cheap single-driver OB's in that setup to test if there is any conflict -- as I'm a true fan of open baffle speakers I can only hope there isn't, no tradeoff to be considered then...

Originally posted by Lynn Olson
Not a bad a idea to start a thread on high-quality 3-speaker stereo. I read Patent #5610986 carefully, and was dismayed to see no definition of the matrix itself, which is a crucial part of the invention. I hold three patents myself, and I know the patent office frowns on partial disclosure - trade secrets and patents are two different ways of protecting intellectual property, and are not to be commingled. I'm not a patent attorney, but that's what they told me. I was told to choose one of three methods: public disclosure in a magazine (creating prior art, thus precluding other patents), trade secrecy with rigorous NDAs for all concerned, and patenting - and not to mix them up.

The lack of disclosure of the 2 -> 3 matrix (which I noted was a static, not dynamic, matrix) makes it hard to tell from a straightforward Gerzon 2 -> 3 system, which dates back to the late Seventies. The Gerzon patents have all expired (along with my own, see #4018992), making them fully-disclosed prior art. I regret to say I do not see full disclosure in #5610986, which seems to invalidate the whole concept of patenting - there should be enough information in the patent so the device can be re-created by one "skilled in the art". Well, I see no mathematical coefficients, just vague descriptions of sum-and-difference networks - which are part of every matrix decoder without exception.

Actually, there's a fair amount of controversy of the correct way to derive the center channel, depending on the goals of the playback system. If the goal is to reduce the amount of comb-filter coloration of centered soloists (which is quite noticeable compared to monophonic single-speaker playback), it doesn't take much level to accomplish this - a phase and dispersion-matched Center speaker 12 dB down will do the job. If a smooth, equal-energy soundstage is desired, then more Center signal is required - but raising the level of the Center speaker also degrades the resolution of far-left or far-right signals due to crosstalk (the center signal is still present, and only a few dB down, when a L-only or R-only signal is on the recording).

This crosstalk is always there with any static matrix - which is why dynamic matrix systems were and are used for Sansui QS Vario-Matrix, Shadow Vector SQ, CBS Paramatrix SQ, Dolby Pro-Logic I, and Dolby Pro-Logic II. Once you go to dynamic playback matrices, of course, then the whole issue of image-shifting and maintaining constant reverberation energy raises its head - not to mention suitably-chosen attack and decay time constants for dynamic matrix (typically 1~3 mSec attack and 20~50 mSec decay).

Going back to static-matrix systems - which probably have the least coloration and odd-sounding dynamic artifacts - the requirement for phase, amplitude, FR, and dispersion-matching for every loudspeaker become quite severe, since there is never very much signal separation with any kind of input signal. With only 3~6 dB of separation between any pair of speakers - at the very most - then small differences between speakers become very important. Of course, even with full-discrete signals, it's still important, but only for the phantom images (and the reverberant content).

Originally posted by KSTR
Hi Lynn,

Um, I'm a bit bewildered from your comments to be honest. I for one had no difficulty to find the required matrix formulae in the patent, albeit they are not written in classic matrix form. It's all right on the front page:
Lout = Lin - m*Rin
Rout = Rin - m*Lin
Cout = (1-m)*(Lin+Rin)

In the more general form one replaces (1-m) with another factor n and then we have all degrees of freedom in useful 2-to-3 linear revectorizing (as it is put sometimes). With these two factor I played a lot, and found, confirming the results of Mr.Miles and Mr.Bongiorno, that both factors at ~0.5 gives the best results (and, btw before I learned about the Miles patent). I also have two working circuits and some ideas for "high-end" circuit variations.

I hope we can start a serious, fruitful but relaxed(!) discussion, maybe even users (if there are any reading this forum) of the MilesTech ("Multisonic Imager") or Bongiorno ("Trinaural") devices can give some input.

- Klaus

[Lynn Olson]

In reading the patent, it was the definition of "M" that had me puzzled - with the "M" term omitted, there's no matrix at all, just ordinary stereo. The entire patent hinges on what "M" is defined to be.

Static sum-and-difference matrices are covered by Scheiber's papers in the AES Journal in the early 1970's, and many combinations and permutations (including 2 -> 3) are described. The Gerzon papers, although the math is much more opaque, are a greatly expanded superset of the Scheiber work, with sophisticated correction for distance effects, height-illusion, and interchannel phase compensation.

I urge anyone that is interested in the static-matrix multichannel decoders to read the papers in the AES Journal in the mid-Seventies, with a focus on papers by Scheiber, Gerzon, and the team at Denon. These cover just about every imaginable permutation of N -> M channel decoders, including full-height 3D systems - far beyond anything commercially available today, in any format.

That said, static-matrix systems using a sine-cosine decoding law for each channel are well worth exploring. The oldest and most obvious is the Klipsch system of:

+1.0 Left In, 0.0 Right In = Left Out
+0.707 Left In, +0.707 Right In = Center Out
0.0 Left In, +1.0 Right In = Right Out

which can be refined to:

+0.966 Left In, -0.259 Right In = Left Out
+0.707 Left In, +0.707 Right In = Center Out
-0.259 Left In, +0.966 Right In = Right Out

Looking at a Scheiber sphere, the Klipsch matrix has decoding points 90 degrees apart (L,C,R) with the rear quadrant silent (this gives a front-biased presentation since rear reverberation is not decoded). The refined matrix has decoding points 120 degrees apart, giving equal energy decoding across the Scheiber sphere, without the frontal bias of the Klipsch matrix.

In the refined matrix, antiphase crosstalk in the Left and Right speaker gives a degree of compensation for the crosstalk emanating from the Center speaker (antiphase crosstalk pushes the image outside the stereo pair, unlike normal inphase crosstalk, which pushes the image towards the center). There is also a much stronger sensation of front-to-back movement, with reverse-phase content on the recording stimulating the Left and Right speakers, and leaving the Center silent.

I hope people explore these 3-speaker systems - no reason why not, since many of the earliest stereo recordings were originally made in 3-channel format, and would benefit from 3-channel playback. I'm pretty sure the Center level needs to be adjusted for recording technique, though - just a whisper for true-Blumlein recordings, a little more for ORTF-style crossed-cardioids, and "normal" level for pan-potted and multimiked recordings.

A good way to assess the overall quality of the system is pan a pink-noise source across the soundstage. There should be no changes in timbre as the pink-noise is slowly panned - in most systems, though, you'll hear odd colorations as the sound moves. The goal of a 2 -> 3 static matrix is to minimize the coloration as the pink-noise is panned - this requires phase-matched loudspeakers with identical polar patterns and the Center channel at just the correct level.

P.S. Note that 2 -> N channel matrices all come down to: Left In (math operation) + Right In (different math operation) = Output. Repeat for each output channel, using different pairs of operators.

Sometimes the math operation is nothing more than a simple level shift and/or polarity inversion, sometimes there's a phase-shift network in there, and sometimes there's a dynamic decoding element that senses where the max loudness "should" be and re-shapes the matrix dynamically to follow the loudest sound around the room.

[KSTR]

Originally posted by Lynn Olson
I urge anyone that is interested in the static-matrix multichannel decoders to read the papers in the AES Journal in the mid-Seventies, with a focus on papers by Scheiber, Gerzon, and the team at Denon. These cover just about every imaginable permutation of N -> M channel decoders, including full-height 3D systems - far beyond anything commercially available today, in any format.

Yes, Michael Gerzon was a truly amazing person. I have most of his patents lying around somewhere, as well as other papers. Some very readable material (little to no math involved) can be found here:
http://www.audiosignal.co.uk/Gerzon%20archive.html

That said, static-matrix systems using a sine-cosine decoding law for each channel are well worth exploring. The oldest and most obvious is the Klipsch system of:

+1.0 Left In, 0.0 Right In = Left Out
+0.707 Left In, +0.707 Right In = Center Out
0.0 Left In, +1.0 Right In = Right Out

which can be refined to:

+0.966 Left In, -0.259 Right In = Left Out
+0.707 Left In, +0.707 Right In = Center Out
-0.259 Left In, +0.966 Right In = Right Out

Looking at a Scheiber sphere, the Klipsch matrix has decoding points 90 degrees apart (L,C,R) with the rear quadrant silent (this gives a front-biased presentation since rear reverberation is not decoded). The refined matrix has decoding points 120 degrees apart, giving equal energy decoding across the Scheiber sphere, without the frontal bias of the Klipsch matrix.

In the refined matrix, antiphase crosstalk in the Left and Right speaker gives a degree of compensation for the crosstalk emanating from the Center speaker (antiphase crosstalk pushes the image outside the stereo pair, unlike normal inphase crosstalk, which pushes the image towards the center). There is also a much stronger sensation of front-to-back movement, with reverse-phase content on the recording stimulating the Left and Right speakers, and leaving the Center silent.

I saw these decodings etc in the WWW somewhere recently, unfortunately I can't remember where -- I think I even saved them, only to be lost in Gigabytes of my HardDisk jungle (*arrgggh*).

Now my point is that these decondings will surely work very well with material produced for it. Normal stereo recordings are more likely produced to work within the 2-channel reproduction domain, speakers at +-30deg angles. So the soundstage/imaging illusion will be distorted, out of proportions, and not be what the producer had originally in mind. This is because recording techniques have been empirically optimized to work within that 2Ch, +-30deg paradigm. There is excellent work from Eberhard Sengpiel on these matters (a renowned -- grammy awarded -- classical sound engineer and unversity professor). Unfortunately it's available in german only. Localization cues come from interchannel level (dL) and time (dT) differences. Equal signs of dT and dL denominate like differences, with ie the louder sound also being earlier. According to the work of Sengpiel we can express approximized statistical localization b (ranging from 0% to 100% of left or right, 0% meaning centered) of wideband sources as follows, with like dL/dT:
b(dL, dT) = b1(dL) + b2(dT)
b1(dL) = 1.72935e-4*dL^4 - 4.932668e-3*dL^3 - 0.148525*dL^2 + 8.818633*dL
b2(dT) = 21.090084*dT^4 - 61.293151*dT^3 + 17.099029*dT^2 + 107.74868*dT
(dL in dB and dT in ms units).

Therefore, the goal of a rematrixing that wants to be compatible to normal stereo in imaging must try to preserve these relationsships between recorded dT/dL and corresponding localization as much as possible. This is what a matrix factor of ~0.5, together with 45deg spacings between equidistant speakers, does quite well. I tested that with pink noise bursts with various dL/dT relationships including the trading region (different signs of dL and dT). It is not identical, though, but quite compatible. Eventuelly, decated recordings for rematrixed playback deems necessary, with new empirical research on how dL/dT results in localization with that specific scheme.

I hope people explore these 3-speaker systems - no reason why not, since many of the earliest stereo recordings were originally made in 3-channel format, and would benefit from 3-channel playback. I'm pretty sure the Center level needs to be adjusted for recording technique, though - just a whisper for true-Blumlein recordings, a little more for ORTF-style crossed-cardioids, and "normal" level for pan-potted and multimiked recordings.

First, I think we should not mix true 3-channel recordings/playback with the 2-->3 rematrixing issue here. I noted the necessity of the mentioned adjustment indeed, together with some interesting effects of phantom image size/precision: The more dT dominates interchannel differences there more diffuse phantom images become, compared to conventional stereo. Also with true-AB (zero dL, L and R components identical but delayed in time) some degradation in timbre takes places, because of the apparent (and distinct) comb filter effects of the summing in all three channels which do not perfectly compensate each other acoustically. OTOH, with mainly dL and no or little dT content (as with any true XY-recording and close-miked/panpot stereo) images generally sharpen, seemingly because real and phantom sources change roles: Mono centered signals are (dominantly) a real source from the center while L-only or R-only signals now get phantomend with center contribution plus antiphase side contribution. This leads to my impression that the spatial stereo illusion with most recordings gets more convincing, soloists being smack center while ambient info (which is basicly uncorrelated L/R-only signals) gets more of a true ambient character because it is more diffuse. This more convincing seperation between direct and reverberant sound, together with the better correlation of true vs phantom sources to the typical weighting of soloist vs comping in most music and recording styles makes one of the main improvements of that specific rematrixing. The other being the more invariant and stable sweetspot w.r.t. sideway head movement and especially head turn (where the normal stereo quickly deteriorates). The sweetspot is way shorter, though, as soon as you leave the equidistant zone (L/R vs C) the top registers start to fall apart in the imaging.

A good way to assess the overall quality of the system is pan a pink-noise source across the soundstage. There should be no changes in timbre as the pink-noise is slowly panned - in most systems, though, you'll hear odd colorations as the sound moves. The goal of a 2 -> 3 static matrix is to minimize the coloration as the pink-noise is panned - this requires phase-matched loudspeakers with identical polar patterns and the Center channel at just the correct level.

This assessment process is exactly how I did my correction to account for the different speakers I had to use. I would lessen the statement "no changes in timbre" to "natural changes in timbre", corresponding to the timbre changes of a real mono source, moving between speakers (have you SO carry a speaker around while your listening ;-). Of course I could not do that to perfection, and therefore I can back the rigorous requirement of truly identical speakers in every regard (including precise equidistant setup, with a point some inches in front of one's nose as the center point) plus well balanced room acoustics. Both is also required for normal stereo, so this is not a specific point of rematrixed stereo.

- Klaus

[Lynn Olson]

You bring up a very good point. Any type of sum-and-difference matrixing is going to have a profound impact on signal content with interchannel time differences (dT). In the simplest case, a solo instrument picked up by two spaced microphones, when played back on two loudspeakers with near-infinite electrical separation, each speaker only plays one signal.

Once the signal is processed through a sum-and-difference matrix, what was one now becomes two - and the newly created time-delayed signal may become polarity-reversed thanks to the matrix. Since real-world reflections and echoes preserve polarity, these polarity-reversed dT signals become an unusual, electronically-created coloration not found in nature. An all-acoustical recording system, for example, could not create this coloration.

Things are pretty benign for synthetic stereo created with mono mike feeds pan-potted to various locations in the soundstage - there are no correlated dT signals to contend with. These colorations appear when there are (multiple) spaced microphones picking up the same instrument - almost unavoidable with contemporary classical recording, but not that uncommon in pop music (for some instruments).

With uncorrelated dT signals (from a reverb plate), probably not much problem - but classical recording with a forest of microphones that have levels bounced up and down to "zoom into" groups of musicians would be very difficult for any matrix. I remember back in the Shadow Vector days that classical recordings pretty much baffled the direction-sensing matrix system - the phase cues weren't random, but semi-correlated with the music in a very annoying way.

It's interesting that two-speaker playback essentially conceals the mike technique, as the producer intended. Once sum-and-difference matrixing is used, though, any dT content acts on the matrix in an unpredictable way, creating phantoms in unexpected locations, as well as odd colorations due to electrical comb-filtering.

[dobias]

I found one of my previous attempts at having a center speaker. It was the Dynaco QD-1 control box. While it also attempted to facilitate rear speakers, I didn't use that part of the control this time. I believe it is basically the old Klipsch wiring setup.
After wiring it up I tried setting the center speaker volume control.

The phantom center speaker was so pronounced with the open baffles there was no noticeable benefit with the center speaker.
After I spread the left & right speakers farther apart the center speaker had more effect.

The left & right speakers are now 11 feet apart & each is 10 feet to a point in front of the sweet spot making an isoceles triangle. The center speaker volume is now at a minimum setting.

Mea Culpa:
I have the TV high in the corner with the center speaker below. That places the arc of the left & right speakers about 4 feet in front of the TV & center speaker. The couch is at a 45 degree angle with the walls & faces the TV.

All-in-all the results reminded me of Peggy Lee singing "Is that all there is?"
The sound stage did not seem to enlarge or improve.

My next step will be to dispense with the QD-1 & try direct wiring the Klipsch method....as soon as I find out my Audire Crescendo can have the two negative speaker posts connected without harm.

dobias

[KSTR]

Originally posted by Lynn Olson
Things are pretty benign for synthetic stereo created with mono mike feeds pan-potted to various locations in the soundstage - there are no correlated dT signals to contend with. These colorations appear when there are (multiple) spaced microphones picking up the same instrument - almost unavoidable with contemporary classical recording, but not that uncommon in pop music (for some instruments).

I have to admit that in my tests I didn't use material were I could be certain it was recorded in plain farfield A/B (the worst case, only dT, no dL). Besides the various noise signals, the test music was mainly "synthetic" or close-miked panpotted stereo, the usual rock, pop, electronic, jazz combo etc stuff. I would estimate, OTOH, that true A/B-recordings might be rather seldom, because the comb filtering, if significant, would also show up in mono playback, and ususally recordings (at least those carried out by radio-stations or radio network orchestras which is/was common practise in europe) are (still) made with mono compatibility in mind. That said, people who listen mainy to classical music (or whatever produtions with much A/B content) might encounter problems with rematrixed systems. For me, Trinaural worked wonders with electronic stuff like Massive Attack, complex Prog Rock like The Mars Volta and with most live or studio Jazz record I own, with the exception of some solo piano recordings which seemed to sound less natural, probably due to the specific mic setup used.

From a theory standpoint, the acoustical comb filtering at the listeners ears (which is, fortunately, masked quite sufficently by out brains), is different with 2Ch. vs. Trinaural: With 2Ch, it's worst with centered mono phantom sources and inexistent with true side-only signals (one of L or R being zero), while with trinaural it's always a little, the worst point beeing at 6 dB difference for a dL-only signal, then two speakers (center & side) emit at equal levels, while the other side speaker is silent. Signals of this kid are found seldom in a mix, while centered mono phantom and 100% side pan is very commonly used, at least in rock music etc. I speculate that this more constant behaviour is a bit favorable to the all-or-nothing effect spanned by 2Ch playback.

From here :

Originally posted by ro9397
I've extensively auditioned Bongiorno's Tri-naural processor in several good systems. Roger Waters' Ambisonics CD has that special wrap-around effect played back in stereo; in Tri-naural the sound field collapses into mush (only during the Ambisonic wrap-around effect).

I also noticed the incompatibility with HRTF+stereo triangle -based localization effects -- as I happend to have created, a while ago, a simple hobbyist version of Q-sound (which I didn't know about, then) myself, I hence tried that and it failed, and it had to fail with the trinaural decoding. By now, it's a commony known incompatibility of it (one of the few).

So, if we know where the compromises are, we can better choose what might prove to work good for our specific situation.

- Klaus

[KSTR]

OT

Originally posted by dobias
PS: I, too, have had patents (that made fortunes for my employer).
I learned the only good patent is one that can withstand lawsuits.
I defended my patents for 5 years in Federal Courts. In fact I have the dubious distinction of having the last Federal trial , all the way to the Appeals Court, before Patent disputes were resolved by an arbitration board.

I also have a similar situation like that in your first and second sentence. Things in the EU are a bit different, but if you don't have the pocket money to defend your patents in case of a violation, it's useless here also. Sell or be sold....

/OT

- Klaus

[KSTR]

Originally posted by dobias
My next step will be to dispense with the QD-1 & try direct wiring the Klipsch method....as soon as I find out my Audire Crescendo can have the two negative speaker posts connected without harm.

dobias

I hope it will work out for you. You could check that with an ohmmeter (system up, but no signal) and additionally with a AF-millivolt measurement with signals applied. Bridged outputs or other incopatible stuff are not that commonly used, so your chances are good.

- Klaus

[KSTR]

ah, 30min edit limit reached, so you know why there are still typos ;-)

Attached is a damping (in dB) plot for a panpotted signal with the trinaural / optimum linear matrix, m=0.5, panned from center to the left. Blue (inphase section) and turqoise (anti-phase section) is left output, red is center and brown is right output. BTW, the damping at the -6dB pan paoint from the channels is 2.5dB (gain=0.75 each). I think it demonstrates the reasonable (but not perfect) output channel separation.

- Klaus

[KSTR]

"panpotted to the right" it should read.