Hi Jorn, Yes, you’re right. To summarize the process:
- 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). 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. Thinking about it now, it should be very easy to set-up a HOA2binaural conversion like that in REAPER, after getting the filters, by using the ambiX plugins, and setting the decoder matrix to a unity matrix, then convolving the outputs with the FIR filters using the multichannel convolver plugin. If you would like to experiment, I’ll be happy to process some HRTFs and send you the filters. There are various papers on expansion of HRTFs to SHs, Duraiswami, Dylan Menzies, Brungart, Abhayapala, Evans, are some of the names that spring to mind. It is a very convenient way of interpolating HRTFs too at any direction, so two birds with one stone.. About the inter-aural time delay, the complex HRTFs should include that automatically, since they are measured at the ears, “off-centre” for the measuring setup. You can also do it however by the common factorization of splitting the HRTFs into a (directional) inter-aural time difference and a minimum phase filter, expand the minimum phase HRTFs, and then introduce the inter-aural time difference afterwards. About inter-aural time delay and frequency dependence, I think it has been shown that for most practical purposes replacing it with a frequency-independent one does not affect much. You can also express the ITD on SHs, it is a very convenient representation of it, since it really approximates a slightly elongated dipole on the interaural axis, and hence only the first 2-3 orders are enough to describe it well. Regards, Archontis On 25 Feb 2016, at 22:48, Jörn Nettingsmeier <netti...@stackingdwarves.net<mailto:netti...@stackingdwarves.net>> wrote: On 01/27/2016 01:56 PM, Jörn Nettingsmeier wrote: On 01/26/2016 11:05 PM, Politis Archontis wrote: Hi Jorn, yes that is correct. I think however that the virtual loudspeaker stage is unnecessary. It is equivalent if you expand the left and right HRTFs into spherical harmonics and multiply their coefficients (in the frequency domain) directly with the coefficients of the sound scene (which in the 1st-order case is the B-format recording). This is simpler and more elegant I think. Taking the IFFT of each coefficient of the HRTFs, you end up with an FIR filter that maps the respective HOA signal to its binaural output, hence as you said it's always 2*(HOA channels) no matter what. Arbitrary rotations can be done on the HOA signals before the HOA-to-binaural filters, so head-tracking is perfectly possible. Wow. That sounds intriguing, thanks! I'll try to wrap my head around the SH expression of an HRTF set in the coming months, hopefully with the help of Rozenn Nicol's book. Sorry to revive such an old thread, but the AES monograph on binaural technology has arrived, and I've begun to study it. Definitely a great resource, recommended: http://www.aes.org/publications/monographs/ Archontis, I'm still trying to understand how to express a set of HRTFS as a SH series. If I understand correctly, all HRTFS for a given ear can be expressed as a function on the sphere, but it would be frequency dependent. So we'd need an extra degree of freedom there, how does that tie in with Ambisonics? One HRTF "balloon" per frequency bin? Also, how do you express the inter-aural time delay conveniently (which, as I've learned from Rozenn Nicol, depends not only on direction, but also on frequency)? Are there papers out there that describe this in detail? Best, Jörn -- Jörn Nettingsmeier Lortzingstr. 11, 45128 Essen, Tel. +49 177 7937487 Meister für Veranstaltungstechnik (Bühne/Studio) Tonmeister VDT http://stackingdwarves.net _______________________________________________ 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. -------------- next part -------------- An HTML attachment was scrubbed... URL: <https://mail.music.vt.edu/mailman/private/sursound/attachments/20160225/36230812/attachment.html> _______________________________________________ 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.
