On 2012-11-07, Tommaso Perego wrote:
I was wondering how, knowing the diameter of a speaker octagon, using 1st or 3rd Order ambisonics, to calculate precisely the dimensions of the sweet spot area. Any ideas?
There is no unambiguous sweet spot. Even the arbitrarily cut-off, approximative one depends on the precise rig layout and the precise decoder being used.
In general, within the traditional Ambisonic theory, what delimits the sweet spot is the area within which the energy vector magnitude achievable by the rig and the decoder in unison stays above a certain bound. That's because the velocity decode used at lower frequencies is much easier to get right an sich. I'd say this holds at least for the 1st to 3rd orders you're talking about, at least if your rig and decoding solution is close to any of the regular decodes we already know about, and/or has been numerically optimized.
Within those bounds, the sweet spot is a circle (pantophony), or more generally an ellipse (the more general 2D case) or even a general ellipsoid (the 3D, or periphonic case). Its theoretical size does *not* substantially vary above the minimum number of speakers needed for spatially unaliased reproduction at any given order. That metric can be derived directly from the radial Bessel functions associated with each given order, minus any imperfections caused by a discrete rig (minimal with a regular rig, much more if you go towards something like the ITU setup, and pretty bad in the 3D case where you usually have to omit beyond-horizon speakers altogether).
At the same time, the psychoacoustic optimization utilized even by plain old ambisonic works over a much larger area. There the criterion becomes evermore psychoacoustic the further away you go from the center of the rig. What eventually breaks the image, there, is the differential distance to your speakers. There it's the absolute distance to the rig that matters, unlike with the sweet spot proper. What you'd want to mind there is the temporal fusion threshold of incoherent sound sources, which is somewhere in the vicinity of 10-40ms. Above that you'll get separate arrivals/echo, and even if you approach that to within 20%, you'll definitely hear combing.
That sort of stuff then partly (and surprisingly rapidly) goes away at 2nd to 3rd orders because the rig starts to speak only from the direction of the incident sound instead of relying on antiphase signals from the other side. But even then these off-centre effects have to be calculated out in full if you want to know the true extent of the sweet spot: near to rig edge you can still end up with two widely spaced speakers crossing the fusion threshold or combing, especially since at those higher orders, pretty much nobody can afford a dense right even if they can afford high orders, plus pretty much everybody goes to higher orders only when they already decided to do wide areas as well.
Finally, those combing artifacts and the like have additional funky qualities. That's shown in that when you work with first order, the minimum four speakers for pantophony and the minimum six for periphony appear to work the best, unless you can go to tens or even hundreds of speakers. The reason is that while the basic signal set is thoroughly antialiased, a sparse rig still leads to spatial aliasing like combing and even acutely perceived multiple arrivals away from the true diffraction limited sweet spot. It surfaces that when than happens, the fewer arrivals there are, the better it is for our ears, psychoacoustically speaking. So, there is a kind of an unintuitive Laffer curve working here, as far as speaker numbers go: you need the minimum, or sometimes in periphonic work a bit more, but when you go beyond that, you'd better be willing to go at last one or two whole *magnitudes* beyond it before it sounds even as-good.
-- Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front +358-50-5756111, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 _______________________________________________ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
