Nice work!

Dick Duda and Ralph Algazi at UC Davis used a similar array for their
motion-tracked binaural work.  They didn't decode to an ambisonic
representation, but went straight from the microphones to binaural. They
looked at 8, 16, and 32 mic configs, as well as spheres and cylinders as
the scatters.  Dick gave a demo at a San Francisco AES meeting with a
recording of a bluegrass band and it was easily the best binaural sound I
have ever experienced.

Details here:
     Algazi, V. Ralph, Duda, Richard O., Thompson, Dennis M.,
"Motion-Tracked Binaural Sound," J. Audio Eng. Soc., vol. 52, no. 11, pp.
1142-1156, (2004 November.)
https://www.aes.org/e-lib/browse.cfm?elib=13028


Aaron Heller <hel...@ai.sri.com>
Menlo Park, CA US

On Thu, Dec 2, 2021 at 10:33 AM eric benjamin <ericmb...@gmail.com> wrote:
>
> I believe that Nando may have been thinking about reproduction with
> loudspeaker arrays. He has a system with eight loudspeakers on the
> horizontal plane, as do I. So good up to third order. But I actually have
> 24 full-range loudspeakers available. Would it be advantageous to expand
> our systems to higher order? I've been asking this question for a very
long
> time. With higher order program material slowly becoming available,
perhaps
> we can find out.
>
> Eric Benjamin
>
> On Thu, Dec 2, 2021 at 5:57 AM Jens Ahrens <jens.ahr...@chalmers.se>
wrote:
>
> > Hi Fons, hi Nando,
> >
> > Please excuse that I’m responding to both of you in the same mail. There
> > is sufficient overlap in the matters to keep the thread from diverging.
> >
> > @Fons: Thanks for the clarification! We will look into this.
> >
> > @Nando: (The question was what the high orders contribute.)
> >
> > It’s hard to tell how exactly the high orders contribute. One aspect is
> > the interaural coherence that needs to be appropriate. The other main
> > aspect is what I typically term the equalization: Below the aliasing
> > frequency, things are fine anyway. Above the aliasing frequency, the
> > spectral balance of the binaural signals tends to be more even the
higher
> > the orders are that are present. The deviations from the ideal spectral
> > balance also tend to be less strongly dependent on the incidence angle
of
> > the sound if higher orders are present.
> >
> > Much of the angle dependent deviations of the spectral balance can be
> > mitigated, for example, by MagLS so that the perceptual difference
between,
> > say, 7th order and infinite order is small. I can’t tell if it gets any
> > smaller with higher orders. My (informal) feeling is that somewhere
between
> > 5th and 10th order is where the perceptual difference to the ground
truth
> > saturates, both in terms of equalization and the coherence.
> >
> > Best regards,
> > Jens
> >
> >
> >
> > > On 2 Dec 2021, at 11:20, Fons Adriaensen <f...@linuxaudio.org> wrote:
> > >
> > > Hi Jens,
> > >
> > >> I’m attaching Fig. 1 from the JASA article.
> > >
> > > Nothing was attached (or it got lost...)
> > >
> > >> If I’m not misreading, then the 7th order is available somewhere
between
> > >> 2 kHz and 3 kHz and higher. Aliasing kicks in at around 4 kHz-ish.
> > >
> > > So the question is if this small range (less than one octave) actually
> > > contributes anything useful.
> > >
> > >> My guess is that it is not more or less sensitive than SMAs.
> > >
> > > I'd agree.
> > >
> > >> I’m as close as a few centimetres to the surface of the array. This
> > >> triggers a lot of the high orders at low frequencies, and if there
> > >> is something that is not ideal, then the low frequencies tend to go
> > >> through the ceiling.
> > >
> > > If they don't that could just be because their contribution at LF
> > > is filtered out anyway, e.g. if your A/B process includes high pass
> > > filters of an order at least one higher than the order of the
> > > component they act on.
> > >
> > >> How would I be noticing if the microphone mismatch is above
> > >> the tolerance level?
> > >
> > > One way uncalibrated capsule gains will show up is that after
> > > binaural rendering you get significant ILD at LF, which should
> > > never happen except for very close sources.
> > >
> > > This actually happened recently with a binaural rendering system
> > > I was working on. When the room sound (early reflections and
> > > reverb tail) was added, this resulted in excessive ILD at LF,
> > > and a perception of the room sound that was clearly biased to
> > > one side.
> > >
> > > The room sound in this case was from a real room, measured using
> > > an SMA. Analysing these measurements revealed capsule gain errors
> > > up to +/-3 dB. When these were compensated for, the problem
> > > disappeared.
> > >
> > >
> > > You could just measure the B-format polars at LF, but that would
> > > require an anechoic room.
> > >
> > > You could instead compute the theoretical capsule signals for a
> > > set of directions, apply some gain errors, send the result through
> > > your A/B process, and plot the result.
> > >
> > > The only thing that mitigates this problem is statistics: with
> > > a high number of capsules contributing to each harmonic, errors
> > > tend to average out to some extent.
> > >
> > > Ciao,
> > >
> > > --
> > > FA
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