Hi Fons, True, slight mistake! for equiangular grids it should be (N+1)^2<4*Q.
You are absolutely correct about the linearity and the exchange of the order of the transforms. And the virtual loudspeakers approach should be exactly equivalent, and that's the main reason I don't understand why one should use it. In the best case, taking into account that the decoding was done properly, it will just give the same result as doing the conversion directly on the SH domain. The virtual loudspeaker approach essentially takes the HOA signals back to the spatial domain, via decoding, convolves each plane wave with the respective HRTF, and integrates across all directions. Which is done directly in the SH domain by convolving the HOA signals with the HRTF SH coefficients, and summing the results. I don't see the reason for this extra intermediate inverse SHT (decoding) in this case. Regards, 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, -- 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.
