On Fri, Nov 05, 2010 at 07:12:03AM +0100, [email protected] wrote: > the icosahedron (faces) does not provide a uniform spherical sampling in the > sense that the spherical harmonics are orthogonal (well spotted Dave!). > If you look for example at my thesis p. 167 you can observe that with such > distribution the 3rd order (sampled) spherical harmonics are not orthogonal. > I never understood exactly why (though I think Nicolas once told me something > on that line), but I think it boils down to the definition of a uniform (or > regular) sampling on a sphere. > What does it actually mean?? or better, what do we mean by saying that?
I've been asking myself that question as well. > On the other hand, this is an issue if you use the hermitian transpose as an > inverse, but the pseudo-inverse should solve the problem, I believe. It does. But the usual trick of transforming the systematic decode into a max-rE one (a spatial filtering, applying per-degree gain factors), does not work. And the polar patterns corresponding to the systematic decode are not axisymmetric. - this really surprised me and made me question the correctness of my code. > This is what I know about loudspeaker arrangement, but I have no idea how > this > relate to the energy vector thing... > (I don't actually know how this gains are derived... I always see these thing > from a different point of view, that is damping of the singular values of the > matrix you are inverting) I should look into that. > How do you judge the orthogonality of the Sph. Harm. from the Sing Values? I > assume that if the harmonics were orthogonal, the S.V. would be all equal > (apart from the null-space of the pseudo inverse - i.e. S.V.=0, if you allow > me this lack of math. rigour...) Indeed. For the icosahedron, the condition number is still reasonable (around 2.5 IIRC). The three last SV are significantly lower than the rest. Ciao, -- FA There are three of them, and Alleline. _______________________________________________ Sursound mailing list [email protected] https://mail.music.vt.edu/mailman/listinfo/sursound
