On 2011-12-23, Bo-Erik Sandholm wrote:
If you go back in the archives you will find posts where I and Fonz discuss 3 D playback rigs based on having 6 horisontal speakers that can be "reused" when playing back 3D.
As we say in Finnish, "asiasta kukkaruukkuun" ("from the matter (at hand) to pottery" or something like that)...
Every time someone talks on-list about more than four speakers at a time, I get a definite 3D vibe, evenif 6-8 speakers could just comprise a denser than usual pantophonic rig. Then, such speaker counts most *certainly* do not comprise a dense periphonic one; in fact an arbitrary number of them in that range do not give rise to a periphonic rig which is amenable to most forms of stochastic optimization, against the classical reproduction equations. Unless you place them precisely acccording to the two classical ambisonic solutions (regular or opposite pairs), you're going to be in trouble solving for the decoder coefficients.
I wouldn't dare to claim I have a solution to this overall problem, of course. But one part of it interests me above most, and seems to me to be a stepping stone to more general solutions as well: the problem with ill-conditioned decoder matrices. They after all come from too irregularly spaced speakers, either in space, or with regard to the highest order spherical harmonical function being decoded.
In there I somehow feel one of the numerical L^1 optimization methods such as basis pursuit could perhaps be brough to bare, in a dual formulation. Especially because of the connection with the usual L^2 norm, so essential to the HF optimization problem, via regularization.
Has anybody ever worked with something like this? I mean, even if it's numerical and not closed-form, this sort of stuff at least has solid convergence proofs behind it and all. And at least my hind-brain tells me it could lead to a solid, systematic means of controlling undue gain in even highly irregular rigs.
Finally, at time there's been some talk of "forbidden harmonics" in some of the controlled opposites kinda work. Could somebody perhaps tell me how that theory came to be? Because I have a serious feeling it could be systematized and placed into the general framework I seem to be seeing glimpses of, above.
(Good Yule to ya'll, by the way. At the moment I'm looking after some 7-8kg of prime pork, slowly cooking in the oven for our traditional Christmas meal. Also wondering whether my parents will appreciate a full Twilight-saga for one of their presents. :)
-- 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
