On Tue, Mar 26, 2019 at 09:59:45PM +0000, Martin Dupras wrote: > However, no one has answered my question. I will ask again. > > Can someone point me to any published resources that explain the principles > and theoretical equations required to in theory convert from 2nd order > A-format to B-format? I can find resources for 1st order but not for 2nd > order.
First, there is no such thing as a standard 2nd order A-format. All higher order AMB mics I know of use different capsule geometries. Also some are on a solid sphere, some are open, and that changes things as well. Secondly, for second and higher order things become much more complex. One of the reasons for this is that normal capsules don't have much 2nd or higher order components in their polar pattern. Whatever there is are imperfections or the result of diffraction on the mic body. That means you can only obtain the higher order components by exploiting the finite distance between the capsules and any diffraction, and things become very frequency dependent as a result of this. Basically this a system inversion problem, basic matrix maths. The theoretical polar patterns of the mics, or IR measurements in a number of directions, define a matrix. Inverting this matrix and then multiplying the result with another one defining the B-format polar patterns, you obtain the A/B conversion matrix. This sound simple, but in practice it isn't. The inversion will be frequency dependent and ill-conditioned at lower frequencies. The theoretically 'perfect' result won't be usable, it may require extreme gains and amplify noise and small errors in the original data out of proportion. You need to deal with this in a practical way. This is were the 'secret sauce' is, it is a careful balancing act between conflicting requirements. There are some mathematical tricks to help with this but that would lead us very far. The simple ones (presented in some papers) don't work well in practice. The basic theory you'll find in several papers on higher order Ambisonic theory. Warning: this becomes very mathematical, and there is no other way. Ciao, -- FA _______________________________________________ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound - unsubscribe here, edit account or options, view archives and so on.
