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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