On 2021-12-01, Fernando Lopez-Lezcano wrote:
Cool. The correctly recovered harmonics for 7th order span about 1 octave of useful range, if I understand correctly.
I'd argue in order to have proper field reconstruction, you at least need to have aliasing artifacts below the noise floor of hearing, or if you don't expect full reconstruction, then the noise needs to be well-matched to the expected noise floor, and its joint coding. It needs to follow something like rate-distortion theory.
Since that kind of theory comes from information theory, it expects to know all of the possible sources of information, from all round. So, if you know of some 3D information, it will have to be incorporated. In this case, it to my mind hasn't been.
Is it perceptually significant to have 7th order components?
I've heard upto third order, in a research setting, in an anechoic room, using dozens of speakers. So, full periphony. I've also been presented with pantophony in various configurations. (Ville Pulkki is the professor of acoustics and signal processing here; Eero Aro the hard hitting practitioner, and avid Ambisonic amateur, on the broadcasting side of things..)
That 7th order try at pantophonic ambisonics probably is nice, because even the third order is good. Even the third order leads to very good localisation, over the sphere of horizontal directions. Though at the same time, what you're doing here, is seventh order analysis, oversampling, while not doing seventh order transmission: that'd even periphonically lead to a lot more mics than you have. So somehow you're downsampling from what you have. And because you only sample spatially on the equator, that will lead to lots of missampling of obverse wavefronts; say, reverb modes which go up and down. Even of those wavefronts, which hit the near field of the mic, slightly transversely, and excite ringing modes around the sphere transducer.
Those cannot be controlled without a transducer over the poples. Not even theoretically. Which is why ambisonic traditionally leads to gaussian quadrature over the entire sphere: there *anything* at all can be computationally controlled. At least in theory.
Or, in other words, as you add spherical harmonics to your encoding process, how does the spatial perception change?
Exactly. And how does it work if the field exciting your mic contains, physically, components which aren't equatorially symmetric? They *are* going to be there, after all.
Or from the other end, if you start with a 7th order recording and you start truncating the order to lower and lower values in the decoding process, how does the perception of the recording change? Is there a decrease in order for which you can say, "well, that one did not add much, did it?"
Actually this reminds me of how Gerzon (perhaps Craven as well) optimized POA for 5.1 linear decoding. Maybe that's what they do at seventh order now, because Gerzon did it at fifth already.
That leads to rather an unsymmetrical decoding solution. Which would fit with how badly the above matched symmetrical field behaved -- maybe they just don't understand how to do a dual decode, over all of the field, and over the frequencies?
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