On 2021-12-02, eric benjamin wrote:
I believe that Nando may have been thinking about reproduction with loudspeaker arrays. He has a system with eight loudspeakers on the horizontal plane, as do I. So good up to third order.
What is interesting here, to me, is that sampling on the recording side, and reconstruction on the playback side by discrete speakers -- also an instance of sampling in space -- are not the same, and they deteriorate the reconstruction of the soundfield separately. Sampling in recording array and sampling in reconstruction array...I've never really seen them analyzed at the same time, in the same framework. It's always been so that we go to an intermediate domain, which is continuous, with a little bit of wobble angularly, in noise or gain figures, and then back the same way.
It's all whole and good, if you can assume independence in all of the errors on the way. But then, you can't: the above Swedish case which I've been arguing, *certainly* doesn't admit such symmetry or independence assumptions.
So, the statistical asummptions which underlie e.g. Makita theory, and there Gerzon's, don't go through. In particular, since we're dealing with wave phenomena, there is interference to be contended with. That doesn't come through at *all* in statistical analysis, across 2D and 3D analyses; 3D coupling to a 2D sensor is *wildly* uneven, and if you have a box around the sensor, it can be shown that the sensor coupled with its idealized surroundings, can exhibit resonant modes which run off to an infinite degree, within an infinitely small degree, in angle. It will *always* be nasty, at the edge.
But I actually have 24 full-range loudspeakers available. Would it be advantageous to expand our systems to higher order?
When you have those, the next thing is, you need an anechoic chamber, and well-calibrated microphones. I mean, you have the machinery to launch physical signals, in 3D. Now you need measurement machinery to catch what you launched, and a silent space between which doesn't perturb your signals. Is it that not so? ;)
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