Hi Fons,

I think I see your point, but I still believe they are equivalent in any case? 
In the end by having a lower-order sound field recording (eg B-format), than 
the expansion order of the HRTFs at some frequency, the spatial product is 
going to be limited by the sound-field order. If there is a decoding stage in 
the middle, again a fully directional sound will be spread to multiple speakers 
with an amplitude distribution determined by the order of the decoder, and will 
be convolved with multiple HRTFs from the respective virtual directions, 
essentially limiting the spatial resolution of the HRTFs in the same way and to 
the same order. Are you referring to any other effects of going through the 
virtual loudspeaker case that would affect that?

I see though the point of Jorn and Joseph’s of using dual-band (or any other 
more perceptually-tuned) decoder. But i think that can be done also in the 
spherical harmonic domain with no need for virtual decoding, as it would be 
essentially a weighting of the components of each order (or a convolution/ 
smoothing over the sphere).

Regards,
Archontis


> On 27 Jan 2016, at 00:27, Fons Adriaensen <f...@linuxaudio.org> wrote:
> 
> On Tue, Jan 26, 2016 at 10:05:07PM +0000, Politis Archontis wrote:
> 
>> 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 ...
> 
> True, but the problem with this is that it requires quite high
> order at HF (which is where all the binaural magic happens).
> 
> But then you could say that any small set of virtual speakers
> would be inaccurate as well as it can't capture the high order
> dependency of the HRIR. This is true of course. The only reason
> why it works is that it relies on amplitude or ambisonic panning
> between the virtual speakers, just as reproduction via real
> speakers does.
> 
> Ciao,
> 
> -- 
> 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)
> 
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