And I forgot to mention in the previous message that, while I don't see any benefit in the virtual loudspeaker approach, I see benefits in the direct approach. Doing the virtual loudspeaker decoding, you'll need some uniform arrangement of decoding directions that will be most likely of more points than the harmonics, so you'll need more convolutions compared to the minimum of the direct approach (N+1)^2.
I personally find also useful the fact that storing the HRTFs in an SH format gives an efficient and high-resolution interpolation for non-ambisonic binaural panning, one that uses all the measurement data to interpolate and not only the 2-3 surrounding data points (not relevant though to the ambisonic conversion question..) BR, Archontis ________________________________________ From: Sursound [sursound-boun...@music.vt.edu] on behalf of Fons Adriaensen [f...@linuxaudio.org] Sent: 27 February 2016 12:14 To: sursound@music.vt.edu Subject: Re: [Sursound] expressing HRTFs in spherical harmonics On Thu, Feb 25, 2016 at 09:25:48PM +0000, Politis Archontis wrote: > - Measure the HRIRs at Q directions around the listener > - Take the FFT of all measurements > - For each frequency bin perform the SHT to the complex HRTFs, > up to maximum order that Q directions permit (and their arrangement: > for equiangular measurement grids the order is N<=4*Q^2). The ^2 probably should be on N, not Q. > You end up with (N+1)^2 coefficients per bin per ear. > - Take the IFFT for each of the (N+1)^2 coefficients. > You end up with 2x(N+1)^2 FIR filters that can be used > to binauralize your HOA recordings directly. > - To binauralize, convolve each HOA signal with the respective > SH coefficient filter of the HRTF, for each ear, and sum the > outputs per ear. To me it looks like the FFT/IFFT can be factored out. Both FFT and SHT are linear transforms, so their order can be swapped. With H (t,q) the HRIR in direction q: IFFT (SHT (FFT (H (t,q)))) = IFFT (FFT (SHT (H (t,q)))) = SHT (H (t,q)) Now if Q is a set of more or less uniformly distributed directions, the coefficients of a systematic decoder will be very near to just the SH evaluated in the directions Q. So summing the convolution of the decoder outputs with the HRIR is equivalent to the SHT on the HRIR. In other words, this method is just the same as the 'decoding to virtual speakers' one, with Q the set of speaker directions and using a systematic decoder. Ciao, > _______________________________________________ > 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. -- FA A world of exhaustive, reliable metadata would be an utopia. It's also a pipe-dream, founded on self-delusion, nerd hubris and hysterically inflated market opportunities. (Cory Doctorow) _______________________________________________ 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. _______________________________________________ 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.
