Sampo, You'd probably be interested in this paper where Boaz Rafaely constructs an optimization problem for a dual sphere array... B. Rafaely, “The spherical-shell microphone array,” Audio, Speech, and Language Processing, IEEE Transactions on, vol. 16, pp. 740 — 747, May 2008.
I've tried a similar idea to construct a loudspeaker array in our lab. This is a nonlinear problem, but it is very well behaved and allows for mixed order designs and pretty rudimentary geometric constraints: J. Atkins, “Optimal spatial sampling for spherical loudspeaker arrays,” Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on, pp. 97 – 100, 2010. Allowing for any sort of radial variation (instead of the constraint that the transducers lie on the sphere) makes the optimization much less likely to converge to a suitable local-minimum in my experience. Definitely a fun and very hard problem. You'd need a hefty computing cluster just to be able to simulate the near-field scattering effects of different shapes in each trial. Best, Josh On Mon, Jun 27, 2011 at 7:18 PM, Sampo Syreeni <[email protected]> wrote: > On 2011-06-20, umashankar mantravadi wrote: > >> years ago i had asked (several times) this same question and never got a >> satisfactory answer. i thought of two alternate systems. one where the >> sphere is about seven or eight inches across, and the other where the sphere >> is just large enough(about an inch) to mount the capsules. never tried to >> build either of them > > Just as I've wondered for a long time about automatic, approximative and > purely numerical solutions to the decoder problem, the same goes for the mic > array. Can't we somehow optimize the mic array and whatever baffles plus > other obstacles it might contain? > > As you say, we already know mounting mics on top of an opaque sphere is > superior to a free standing differencing scheme. Not only because Fons and > other have argued for the theoretical singularity of the latter scheme. But > also because of the related, practical, empirical fact that that sort of > thing tends to regularize the encoding equations -- something Gerzon already > talked about when referring to Gaussian quadrature in the literature over > the development of the original SoundField. > > Can't we take such physical optimization beyond simple symmetrical > structures such as the ball, now that we have all this computing power? > Especially in the context of mixed order, semi-pantophonic systems? > > Looking at the highly developed theory of sigma-delta converters, it's all > about dividing the labour between what analog and digital domains do best. > In mic design, the analog side would be about placing various, perhaps even > highly intricate, obstacles among the mics, so as to make the eventual array > perform better in average, as an aggregate, and in a way more susceptible to > digital post-processing. Do we have *any* theory on how to optimize for > this, jointly, between the physical and digital domains, then? If not, it > sounds like a weighty dissertation to me. :) > -- > Sampo Syreeni, aka decoy - [email protected], http://decoy.iki.fi/front > +358-50-5756111, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 > _______________________________________________ > Sursound mailing list > [email protected] > https://mail.music.vt.edu/mailman/listinfo/sursound > -- Joshua Atkins Ph.D. Candidate Dept. Electrical Engineering Johns Hopkins University 3400 North Charles Street Baltimore, Maryland 21218 _______________________________________________ Sursound mailing list [email protected] https://mail.music.vt.edu/mailman/listinfo/sursound
