Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-16, Fons Adriaensen wrote:

Absolutely, I’m happy to make that recording available. Give me some 
time for that, I’ll need to adapt the implementation so that it 
outputs the ambisonics signals in a useable format.


The original mic signals would be interesting as well...


I can freely host a few GiB at a time, and a few GiB permanently, if 
something proves interesting. Just ask.

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Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-15, Steve wrote:

Unless I missed part of this thread, a discussion is in order: without 
the opportunity to address the physical acoustics of the space with 
sufficient treatment to "take the room out of the room," I am afraid 
that much of this academic work will not be able to move out of the 
laboratory environment and into exhibition spaces.


As such, which would be the easiest, most effective, and cheapest ways 
to probe/measure the room?

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Re: [Sursound] A 7th-order array with 16 microphones

[Fons Adriaensen]

On Thu, Dec 16, 2021 at 01:18:47PM +, Jens Ahrens wrote:
 
> Absolutely, I’m happy to make that recording available. Give me some
> time for that, I’ll need to adapt the implementation so that it outputs
> the ambisonics signals in a useable format. 

The original mic signals would be interesting as well...


Ciao,

-- 
FA

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Re: [Sursound] A 7th-order array with 16 microphones

[Jens Ahrens]

Hi Fernando,

Absolutely, I’m happy to make that recording available. Give me some time for 
that, I’ll need to adapt the implementation so that it outputs the ambisonics 
signals in a useable format. 

The thing is, though, that the room was very noisy when I made that recording 
so that I’d want to find better content that allows for a more critical 
evaluation. I’ll speak with the guys from the audio communication group at TU 
Berlin who built the array, which was initially meant for motion-tracked 
binaural. I think that they made proper recordings of classical music and the 
like. I’ll see in how far they can share those. I’ll then convert them to 
7th-order ambisonics.

Best regards,
Jens



> On 14 Dec 2021, at 23:19, Fernando Lopez-Lezcano  
> wrote:
> 
> On 12/7/21 2:15 PM, Sampo Syreeni wrote:
>> On 2021-12-02, eric benjamin 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.
> 
> And I actually have access to a 56.8 system[*] (in our "Stage" small concert 
> hall), the main horizontal speaker ring is 20 speakers, so quite a bit more 
> potential spatial resolution than just 3rd order.
> 
>> What is interesting here, to me, is that sampling on the recording side, and 
>> reconstruction on the playback side by discrete speakers -- also an instance 
>> of sampling in space -- are not the same, and they deteriorate the 
>> reconstruction of the soundfield separately. Sampling in recording array and 
>> sampling in reconstruction array...I've never really seen them analyzed at 
>> the same time, in the same framework. It's always been so that we go to an 
>> intermediate domain, which is continuous, with a little bit of wobble 
>> angularly, in noise or gain figures, and then back the same way.
>> It's all whole and good, if you can assume independence in all of the errors 
>> on the way. But then, you can't: the above Swedish case which I've been 
>> arguing, *certainly* doesn't admit such symmetry or independence assumptions.
> 
> Yes, there will be errors created by both the capture process (encoding into 
> ambisonics), and by the imperfections of the playback environment, be it 
> binaural or plain old speaker arrays. The errors will be mixed together...
> 
>> So, the statistical asummptions which underlie e.g. Makita theory, and there 
>> Gerzon's, don't go through. In particular, since we're dealing with wave 
>> phenomena, there is interference to be contended with. That doesn't come 
>> through at *all* in statistical analysis, across 2D and 3D analyses; 3D 
>> coupling to a 2D sensor is *wildly* uneven, and if you have a box around the 
>> sensor, it can be shown that the sensor coupled with its idealized 
>> surroundings, can exhibit resonant modes which run off to an infinite 
>> degree, within an infinitely small degree, in angle. It will *always* be 
>> nasty, at the edge.
>>> But I actually have 24 full-range loudspeakers available. Would it be 
>>> advantageous to expand our systems to higher order?
>> When you have those, the next thing is, you need an anechoic chamber, and 
>> well-calibrated microphones. I mean, you have the machinery to launch 
>> physical signals, in 3D. Now you need measurement machinery to catch what 
>> you launched, and a silent space between which doesn't perturb your signals. 
>> Is it that not so? ;)
> 
> Yup. While an ideal environment is best, we can try to do some testing done 
> in less than ideal circumstances. Let's assume we have some "machinery" in 
> place (reasonable playback environment, reasonable capture tools).
> 
> The question (to me) is really: what do we actually measure once we have the 
> machinery in place? Are there objective criteria that can tell us what is 
> perceptually relevant?
> 
> I would love to have the original 7th order recording that started this 
> thread, so that it could be played in different systems and with different 
> orders (Jens?).
> 
> Or: we can build horizontal arrays (or 3d arrays, for that matter) with N 
> capsules, where N is an ever increasing number.
> 
> What is the number of capsules and encoded order at which it does not make 
> sense to keep adding capsules (and spherical harmonic components). What is 
> the point at which "the incremental perceptual improvement, if any, is very 
> small and does not justify increasing the number of capsules needed to 
> capture higher orders". I know this would not be a black and white hard 
> limit, of course...
> 
> -- Fernando
> 
> [*] https://ccrma.stanford.edu/~nando/publications/stage_grail_2019.pdf
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Re: [Sursound] A 7th-order array with 16 microphones

[Fernando Lopez-Lezcano]

On 12/7/21 2:15 PM, Sampo Syreeni wrote:

On 2021-12-02, eric benjamin 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.


And I actually have access to a 56.8 system[*] (in our "Stage" small 
concert hall), the main horizontal speaker ring is 20 speakers, so quite 
a bit more potential spatial resolution than just 3rd order.


What is interesting here, to me, is that sampling on the recording side, 
and reconstruction on the playback side by discrete speakers -- also an 
instance of sampling in space -- are not the same, and they deteriorate 
the reconstruction of the soundfield separately. Sampling in recording 
array and sampling in reconstruction array...I've never really seen them 
analyzed at the same time, in the same framework. It's always been so 
that we go to an intermediate domain, which is continuous, with a little 
bit of wobble angularly, in noise or gain figures, and then back the 
same way.


It's all whole and good, if you can assume independence in all of the 
errors on the way. But then, you can't: the above Swedish case which 
I've been arguing, *certainly* doesn't admit such symmetry or 
independence assumptions.


Yes, there will be errors created by both the capture process (encoding 
into ambisonics), and by the imperfections of the playback environment, 
be it binaural or plain old speaker arrays. The errors will be mixed 
together...


So, the statistical asummptions which underlie e.g. Makita theory, and 
there Gerzon's, don't go through. In particular, since we're dealing 
with wave phenomena, there is interference to be contended with. That 
doesn't come through at *all* in statistical analysis, across 2D and 3D 
analyses; 3D coupling to a 2D sensor is *wildly* uneven, and if you have 
a box around the sensor, it can be shown that the sensor coupled with 
its idealized surroundings, can exhibit resonant modes which run off to 
an infinite degree, within an infinitely small degree, in angle. It will 
*always* be nasty, at the edge.


But I actually have 24 full-range loudspeakers available. Would it be 
advantageous to expand our systems to higher order?


When you have those, the next thing is, you need an anechoic chamber, 
and well-calibrated microphones. I mean, you have the machinery to 
launch physical signals, in 3D. Now you need measurement machinery to 
catch what you launched, and a silent space between which doesn't 
perturb your signals. Is it that not so? ;)


Yup. While an ideal environment is best, we can try to do some testing 
done in less than ideal circumstances. Let's assume we have some 
"machinery" in place (reasonable playback environment, reasonable 
capture tools).


The question (to me) is really: what do we actually measure once we have 
the machinery in place? Are there objective criteria that can tell us 
what is perceptually relevant?


I would love to have the original 7th order recording that started this 
thread, so that it could be played in different systems and with 
different orders (Jens?).


Or: we can build horizontal arrays (or 3d arrays, for that matter) with 
N capsules, where N is an ever increasing number.


What is the number of capsules and encoded order at which it does not 
make sense to keep adding capsules (and spherical harmonic components). 
What is the point at which "the incremental perceptual improvement, if 
any, is very small and does not justify increasing the number of 
capsules needed to capture higher orders". I know this would not be a 
black and white hard limit, of course...


-- Fernando

[*] https://ccrma.stanford.edu/~nando/publications/stage_grail_2019.pdf
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Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-02, Jens Ahrens wrote:


It’s hard to tell how exactly the high orders contribute.


No, it is not. You can calculate via normal linear field theory, how 
exactly anything contributes. From the field to your ostensibly linear 
sensor, over an ostensibly rigid sphere, upon which your sensors have 
been imbedded.


That's just math. Comlicated field math, to be sure, but eminently 
doable, and deterministic to boot.


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.


So why not give us the geometry of your ball-and-mic-array? We don't 
need any derivative measurement, because given the primary measurement, 
we can calculate yours on our own.


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.


This is already well-known from the WFS work, of them French and German 
friends/fiends of ours. That WFS lot. Only they mostly talk about things 
in rectangular coordinates, whereas us ambisonic fiends do the spherical 
kind.


Going between those two coordinate systems isn't easy. The 
transformation spreads any excitation or normal wave *terribly* badly 
and unintuitively, over the modes of the other representation.


Much of the angle dependent deviations of the spectral balance can be 
mitigated, for example, by MagLS [...]


What is "MagLS"?

[...] so that the perceptual difference between, say, 7th order and 
infinite order is small.


That has been done via 3rd order periphonic, with active decoding, 
already. It certainly needs less channels than straight 7th order 
pantophonic. So what are you doing here, really?


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.


My hearing is that it in fact seems to cohere at about 3rd, or 4th, 
order, periphonically. That's about 16 independent channels over the 
whole sphere. Maybe with active, nonlinear, dynanamic matrix processing, 
as in the case of DirAC.


In the case of 7th order pantophonic processing, the independent 
channels would have to be 14. So rather close in DSP power. And yet at 
the same time, they couldn't come close to isotropy, as in the case of 
3rd degree ambisonics. They couln't come close to the kind of work 
needed for full 3D VR work, vis-a-vis, holding a ferry-wheel or roller 
coaster ride perceptually constant, over the whole ride.


This system would alias, noticeably, unlike full, isotropic ambisonic.
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Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-07, Hannes Helmholz wrote:


(Also: SMA here refers to spherical microphone array)


Thank you for the clarification.

It's not self-evident that it is spherical, though, since it's really 
just circular, by said symmetry.


As a wannabe-mathematician, I kinda worry about the precise topology and 
symmetry. Especially since it does goes to my argument about how oblique 
modes in the acoustic field excite a discrete array of microphones.

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Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-02, eric benjamin 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.


What is interesting here, to me, is that sampling on the recording side, 
and reconstruction on the playback side by discrete speakers -- also an 
instance of sampling in space -- are not the same, and they deteriorate 
the reconstruction of the soundfield separately. Sampling in recording 
array and sampling in reconstruction array...I've never really seen them 
analyzed at the same time, in the same framework. It's always been so 
that we go to an intermediate domain, which is continuous, with a little 
bit of wobble angularly, in noise or gain figures, and then back the 
same way.


It's all whole and good, if you can assume independence in all of the 
errors on the way. But then, you can't: the above Swedish case which 
I've been arguing, *certainly* doesn't admit such symmetry or 
independence assumptions.


So, the statistical asummptions which underlie e.g. Makita theory, and 
there Gerzon's, don't go through. In particular, since we're dealing 
with wave phenomena, there is interference to be contended with. That 
doesn't come through at *all* in statistical analysis, across 2D and 3D 
analyses; 3D coupling to a 2D sensor is *wildly* uneven, and if you have 
a box around the sensor, it can be shown that the sensor coupled with 
its idealized surroundings, can exhibit resonant modes which run off to 
an infinite degree, within an infinitely small degree, in angle. It will 
*always* be nasty, at the edge.



But I actually have 24 full-range loudspeakers available. Would it be 
advantageous to expand our systems to higher order?


When you have those, the next thing is, you need an anechoic chamber, 
and well-calibrated microphones. I mean, you have the machinery to 
launch physical signals, in 3D. Now you need measurement machinery to 
catch what you launched, and a silent space between which doesn't 
perturb your signals. Is it that not so? ;)

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Re: [Sursound] A 7th-order array with 16 microphones

[Hannes Helmholz]

The audacity on this mailing list is incredible. I am not only referring to the 
last respondent. Questions and discussions could be nice and fruitful. But why 
not some humility and decency?!

On 2021-12-07, 21:19, "Sursound on behalf of Sampo Syreeni" 
 wrote:

> I don’t actually think that there are any special requirements.

I think there are. And you know, I think you came to the right place: we 
might even be able to tell you where you're wrong, where you're right, 
and help you measure and quantify what your product is really about.

Sursounders really like products of your kind to hit the market. They're 
just the *thingy*, in our beloved technology. It's just that we like to 
know what they're about, and how to make them the best they can be. 8)

Right, well the shown work is not a product. Therefore, you're welcome to work 
with or on the method yourself. Recent publications on the work are out there. 
Also, code was made available to allow for direct reproducibility.

@Sampo
So actually, all the interesting questions you're demanding to be answered, you 
could investigate them yourself and report the results!
(Also: SMA here refers to spherical microphone array)

Kind regards,
/Hannes

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Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-02, Fons Adriaensen wrote:

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.


1-2 (atmost 3-) kHz is the so called phoneme range. In there both 
spectral contour and synchronized neural firing of the auditory neurons, 
(via subharmonics, and en masse, because ne firing rate of few neurons 
goes above a kilohertz), helps us to hear what kind of an implement or 
person a sound comes from. That particular range actually serves a known 
and useful function, even if it doesn't constitute *it'll*.



My guess is that it is not more or less sensitive than SMAs.


Again, what is an SMA?
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Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-01, Fernando Lopez-Lezcano wrote:

Cool. The correctly recovered harmonics for 7th order span about 1 
octave of useful range, if I understand correctly.


I'd argue in order to have proper field reconstruction, you at least 
need to have aliasing artifacts below the noise floor of hearing, or if 
you don't expect full reconstruction, then the noise needs to be 
well-matched to the expected noise floor, and its joint coding. It needs 
to follow something like rate-distortion theory.


Since that kind of theory comes from information theory, it expects to 
know all of the possible sources of information, from all round. So, if 
you know of some 3D information, it will have to be incorporated. In 
this case, it to my mind hasn't been.



Is it perceptually significant to have 7th order components?


I've heard upto third order, in a research setting, in an anechoic room, 
using dozens of speakers. So, full periphony. I've also been presented 
with pantophony in various configurations. (Ville Pulkki is the 
professor of acoustics and signal processing here; Eero Aro the hard 
hitting practitioner, and avid Ambisonic amateur, on the broadcasting 
side of things..)


That 7th order try at pantophonic ambisonics probably is nice, because 
even the third order is good. Even the third order leads to very good 
localisation, over the sphere of horizontal directions. Though at the 
same time, what you're doing here, is seventh order analysis, 
oversampling, while not doing seventh order transmission: that'd even 
periphonically lead to a lot more mics than you have. So somehow you're 
downsampling from what you have. And because you only sample spatially 
on the equator, that will lead to lots of missampling of obverse 
wavefronts; say, reverb modes which go up and down. Even of those 
wavefronts, which hit the near field of the mic, slightly transversely, 
and excite ringing modes around the sphere transducer.


Those cannot be controlled without a transducer over the poples. Not 
even theoretically. Which is why ambisonic traditionally leads to 
gaussian quadrature over the entire sphere: there *anything* at all can 
be computationally controlled. At least in theory.


Or, in other words, as you add spherical harmonics to your encoding 
process, how does the spatial perception change?


Exactly. And how does it work if the field exciting your mic contains, 
physically, components which aren't equatorially symmetric? They *are* 
going to be there, after all.


Or from the other end, if you start with a 7th order recording and you 
start truncating the order to lower and lower values in the decoding 
process, how does the perception of the recording change? Is there a 
decrease in order for which you can say, "well, that one did not add 
much, did it?"


Actually this reminds me of how Gerzon (perhaps Craven as well) 
optimized POA for 5.1 linear decoding. Maybe that's what they do at 
seventh order now, because Gerzon did it at fifth already.


That leads to rather an unsymmetrical decoding solution. Which would fit 
with how badly the above matched symmetrical field behaved -- maybe they 
just don't understand how to do a dual decode, over all of the field, 
and over the frequencies?

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Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-01, Marc Lavallée wrote:

With a bit of algebra, f_a = c  N / ( R 2 pi ). So a smaller radius 
for the sphere would improve f_a? Was 0.0875 m chosen in order to 
embed some hardware?


By the way, I think it would be nice to talk about the two different 
forms of spatial aliasing: that which manifests in linear coordinates, 
as in WFS, and that in spherical coordinates, as in HOA.


Those two means of analyzing spatial aliasing are not at all the same, 
and cannot be neatly put into conjunction. If you try to do it, the 
necessary, intermediary functions are rather special, and difficult to 
the hilt to master. You'll immediately go into something like 
Glegst-Gordan coefficients, which ain't nice.


Even proper mathematicians shy away from that stuff, unless *absolutely* 
necessary. :/

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Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-01, Jens Ahrens wrote:

For this type of array, the spatial aliasing frequency f_a is 
dependent on order N and radius R of the array in the exact same 
manner like with spherical microphone arrays (SMAs): N = (2 pi f_a / 
c) R


But it is also dependent on the angle of incidence above the equatorial. 
In wideband theory, if a plane wave hits a ring of discrete sensors just 
right, obliquely, from the third dimension, there is hell to pay in 
aliasing.


And of course there's the near, reactive field to consider, with your 
sort of hard core sensor. Monopoles on top of a rigid sphere, right? The 
fields near a hard ball, and their equivalent far fields in free space, 
under Sommefeld, are highly nontrivial, and they couple lateral to 
vertical field components. Such near fields can of course be symmetric 
over the equator, but only as long as the overall acoustic field is 
symmetric that way, too.


In practice it never is. No source, or ambient reflector, like a room, 
never is. No source really lies on the equatorial plane. And also, if 
I'm not thoroughly mistaken, the sampling over the sphere, and the 
sphere-induced near field, amplify the problems.



  0th and 1st order are available for all frequencies.
  2nd order approx. above 200 Hz
  3rd order approx. above 500 Hz
  etc.


You mean the cutoff, right? Do you quantify the bands in rise above the 
equator, too?


I cannot comment on calibration requirements because we did calibrate 
the array…


Against which precise standard? Over the whole of the sphere of 
directions?



(Nor did we measure how well it was calibrated out-of-the-box.).



Which you should. :)


I don’t actually think that there are any special requirements.


I think there are. And you know, I think you came to the right place: we 
might even be able to tell you where you're wrong, where you're right, 
and help you measure and quantify what your product is really about.


Sursounders really like products of your kind to hit the market. They're 
just the *thingy*, in our beloved technology. It's just that we like to 
know what they're about, and how to make them the best they can be. 8)


As before, much of the physical limitations are qualitatively (and 
also quantitively) similar to SMAs.


Pray tell, what is a SMA?
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Re: [Sursound] A 7th-order array with 16 microphones

[Sampo Syreeni]

On 2021-12-01, Jens Ahrens wrote:

We would like to make you aware of the concept of equatorial 
microphone arrays, which use a spherical scattering body and 
microphones along the equator of that body. Here’s a 3-minute video of 
a binaural rendering of the signals from such array: 
https://youtu.be/95qDd13pVVY


Impressive, but of course 7th order horizontal-to-binaural always is. 
The auditory parallax you demonstrate by speaking close to the array is 
especially convincing.


What isn't so convincing is the performance to the back. There's 
something wonky going on there, because the soundscape is easily heard 
to be pulling in. Are you sure your HRTF's are symmetrical, as befits a 
hard spherical array? Or did you instead start with something like 
KEMAR-data, which would make the array inherently asymmetrical.


I also ask this because where you do the dual test of turning the array 
and moving the source at the same time, I can *definitely* hear skew in 
the field. Maybe even a quadrupole moment. That might suggest your 
algorithms are turning the spherical harmonics the wrong way around; 
not dually as they should be, but something else.


Finally, I'd like to hear this done with extremely wideband and 
impulsive sources as well. A soft speaking voice ain't gonna cut it as 
a test. I'd like to hear balloons being popped, triangles being rung, 
small tambourines being pounded. And at the other end of the spectrum, 
the lowest notes of an organ, to measure how the sensor fairs in 
reactive fields. In particular, what happens above the equatorial plane: 
does the sensor adequately and reliably mitigate the spatial aliasing 
which *necessarily* comes with off-plane waves, over the entire 
frequency range, of it.


It *can* theoretically do something like that, even in the linear 
regime. That's just about joint spatial-temporal domain regularization. 
About taming the off-sightline, aliasing modes, over time-frequency, 
enough to make the thing seem isotropic, over a wide band. You blur out 
where there would be aliasing in direction, you not blur where there's 
symmetry enough to not do that.


Now, if you do something besides this, tell us what it is. There's all 
sorts of work to be done in the nonlinear, machine learning, whatnot, 
work. "Superresolution" it's called, including all of the active 
decoders of the analogue era, like Dolby Surround's Active Matrix, and 
the lot. All of that could be done much better now, using AI methods and 
statistical learning, target tracking algorithms, and whatnot. If you're 
doing those, do tell, I'd be highly interested.


But right now, I don't really see what is so special about the array. It 
sounds like a conventional horizontal array, on a rigid sphere, and then 
jsut conventional processing into a binaural playback. That sort of 
thing has been done in the ambisonic ambit for decades. I've even heard 
in free air better simulacrums of duality, with POA.


So, why not publish your equations and methodology? Let's read back 
from there. :)


Their main advantage over conventional spherical microphone arrays is 
the fact that they require only 2N+1 microphones for Nth spherical 
harmonic order (conventional arrays require (N+1)^2 microphones). The 
price to pay is the circumstance that the array does not capture the 
actual sound field but a horizontal projection of it.


In fact you don't capture a horizontal projection. The only way you 
could do that is with an infinite vertical stack of microphones on a 
stiff cylinder, sensitive to only plane waves. In here, the soundfield 
about the spherical sensor will very much be sensitive to sound from 
above -- as you showed in the video.


That sound will be sensitive to directional aliasing. We just don't hear 
it, because you talk to the mic array in a muffled speaking tone. 
Wideband signals of the like I suggested, would spatially alias widely, 
leading to a *lot* of audible artifacts, direction reversals, and the 
like, when the source and/or the array is made to revolve.


This poses the question of what it may sound like if the array 
captures sound that originates from outside of the horizontal plane?!?


The video is going to demonstrate this!


Now test it the way I wanted, and give us the results. It's going to 
fail, because it's not isotropic. ;)


Though, maybe it's not *supposed* to be isotropic. When you go about it 
that way, it's going to be a kind of periphonic array. In that role it 
probably will perform well. It's just that you can't use that sort of 
array in anything but a free field. In confined spaces, sound does not 
propagate in two dimensions, but in three, with there being coupled 
modes between the 2D and 3D fields. If you try to capture those with any 
anisotropic probe, there will be interplay across dimensions. For 
instance, reverberation will be diminished because it spreads out into 
the third dimension, which isn't being captured, and if there's a 
standing oblique mode in

Re: [Sursound] A 7th-order array with 16 microphones

[Aaron Heller]

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 
Menlo Park, CA US

On Thu, Dec 2, 2021 at 10:33 AM eric benjamin  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 
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  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

Re: [Sursound] A 7th-order array with 16 microphones

[eric benjamin]

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  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  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
> >
> > ___
> > 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.
>
> ___
> Sursound mailing list
> Sursound@music.vt.edu
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> edit account or options, view archives and so on.
>
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Re: [Sursound] A 7th-order array with 16 microphones

[Jens Ahrens]

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  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
> 
> ___
> 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.

___
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account or options, view archives and so on.

Re: [Sursound] A 7th-order array with 16 microphones

[Fons Adriaensen]

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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Re: [Sursound] A 7th-order array with 16 microphones

[Fernando Lopez-Lezcano]

On 12/1/21 12:35 PM, Jens Ahrens wrote:

Hi Fons,

I’m attaching Fig. 1 from the JASA article. Please refer to the article itself 
if the image does not get through. It compares the SMA radial filters with the 
EMA radial filters. Whenever the solid lines deviate from dashed ones of the 
same color, then the given order is not available at the frequency range where 
the deviation occurs. 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, indeed, there is not much more than 7th order that can be squeezed out of 
an array of this radius.


Cool. The correctly recovered harmonics for 7th order span about 1 
octave of useful range, if I understand correctly.


Is it perceptually significant to have 7th order components? Or, in 
other words, as you add spherical harmonics to your encoding process, 
how does the spatial perception change?


Or from the other end, if you start with a 7th order recording and you 
start truncating the order to lower and lower values in the decoding 
process, how does the perception of the recording change? Is there a 
decrease in order for which you can say, "well, that one did not add 
much, did it?"


Just curious...
-- Fernando



Regarding the calibration: Sorry for the imprecise wording! I meant to say that 
we didn’t check if there was actually any mismatch between the microphones. 
(This means in turn that I can't tell in how far the method is sensitive to 
that. My guess is that it is not more or less sensitive than SMAs.)
The reason why I’m not worried is because the array passed the stress test: 
When recording sound sources at a distance of, say, a few meters or farther, 
the whole setup is rather forgiving. That means, for example, that one doesn’t 
need to be too precise in the modelling of the scattering off the microphone 
baffle etc. The critical case is very close sources. Recall that in the video, 
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. We tested 
this with the array, and it behaved.

How would I be noticing if the microphone mismatch is above the tolerance level?

Best regards,
Jens



On 1 Dec 2021, at 17:47, Fons Adriaensen 
mailto:f...@linuxaudio.org>> wrote:

Hi Jens,

Thanks for your reply.

The lower end is limited by the radial filter gain that the user chooses.

The radial filters are not the same like with SMAs, but they are very similar 
so that the limitations are the same.

   0th and 1st order are available for all frequencies.
   2nd order approx. above 200 Hz
   3rd order approx. above 500 Hz
   etc.

It's the 'etc' I'm interested in...

The gain required at LF increases by 6 * order dB for each octave going
down, which in turn means that for a given maximum gain the LF limit
goes up with order. Which makes me wonder if for order > 4 anything
useful actually remains.

I cannot comment on calibration requirements because we did calibrate
the array… (Nor did we measure how well it was calibrated out-of-the-box.).

Does the 'nor' mean you did _not_ calibrate it ?

I don’t actually think that there are any special requirements.

There are.

The required gain (at LF) means that small differences in capsule
sensitivity are amplified as well, and this distorts the resulting
polar pattern.

The simplest possible example would be a first order component X
being produced from the difference of two omni capsule signals
A and B, so

  X = (A - B) * (1 + j (F0 / F))

where F0 will depend on the distance between the capsules.

Now if A has actually 1 dB more gain the difference signal becomes

  1.12 * A - B = (A - B) + (0.12 * A)

The second term, amplified by the filter for low F, will add
an omni component to X.

So the maximum gain that can be used depends not only on how
much noise can be tolerated, but also on the calibration
accuracy (and long term stability) of the capsule gains.


Ciao,

--
FA







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Re: [Sursound] A 7th-order array with 16 microphones

[Jens Ahrens]

Hi Fons,

I’m attaching Fig. 1 from the JASA article. Please refer to the article itself 
if the image does not get through. It compares the SMA radial filters with the 
EMA radial filters. Whenever the solid lines deviate from dashed ones of the 
same color, then the given order is not available at the frequency range where 
the deviation occurs. 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, indeed, there is not much more than 7th order that can be squeezed out of 
an array of this radius.

Regarding the calibration: Sorry for the imprecise wording! I meant to say that 
we didn’t check if there was actually any mismatch between the microphones. 
(This means in turn that I can't tell in how far the method is sensitive to 
that. My guess is that it is not more or less sensitive than SMAs.)
The reason why I’m not worried is because the array passed the stress test: 
When recording sound sources at a distance of, say, a few meters or farther, 
the whole setup is rather forgiving. That means, for example, that one doesn’t 
need to be too precise in the modelling of the scattering off the microphone 
baffle etc. The critical case is very close sources. Recall that in the video, 
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. We tested 
this with the array, and it behaved.

How would I be noticing if the microphone mismatch is above the tolerance level?

Best regards,
Jens



On 1 Dec 2021, at 17:47, Fons Adriaensen 
mailto:f...@linuxaudio.org>> wrote:

Hi Jens,

Thanks for your reply.

The lower end is limited by the radial filter gain that the user chooses.

The radial filters are not the same like with SMAs, but they are very similar 
so that the limitations are the same.

  0th and 1st order are available for all frequencies.
  2nd order approx. above 200 Hz
  3rd order approx. above 500 Hz
  etc.

It's the 'etc' I'm interested in...

The gain required at LF increases by 6 * order dB for each octave going
down, which in turn means that for a given maximum gain the LF limit
goes up with order. Which makes me wonder if for order > 4 anything
useful actually remains.

I cannot comment on calibration requirements because we did calibrate
the array… (Nor did we measure how well it was calibrated out-of-the-box.).

Does the 'nor' mean you did _not_ calibrate it ?

I don’t actually think that there are any special requirements.

There are.

The required gain (at LF) means that small differences in capsule
sensitivity are amplified as well, and this distorts the resulting
polar pattern.

The simplest possible example would be a first order component X
being produced from the difference of two omni capsule signals
A and B, so

 X = (A - B) * (1 + j (F0 / F))

where F0 will depend on the distance between the capsules.

Now if A has actually 1 dB more gain the difference signal becomes

 1.12 * A - B = (A - B) + (0.12 * A)

The second term, amplified by the filter for low F, will add
an omni component to X.

So the maximum gain that can be used depends not only on how
much noise can be tolerated, but also on the calibration
accuracy (and long term stability) of the capsule gains.


Ciao,

--
FA







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Re: [Sursound] A 7th-order array with 16 microphones

[Fons Adriaensen]

Hi Jens,

Thanks for your reply.

> The lower end is limited by the radial filter gain that the user chooses.

The radial filters are not the same like with SMAs, but they are very similar 
so that the limitations are the same. 
> 
>0th and 1st order are available for all frequencies. 
>2nd order approx. above 200 Hz
>3rd order approx. above 500 Hz 
>etc.

It's the 'etc' I'm interested in...

The gain required at LF increases by 6 * order dB for each octave going
down, which in turn means that for a given maximum gain the LF limit 
goes up with order. Which makes me wonder if for order > 4 anything
useful actually remains.

> I cannot comment on calibration requirements because we did calibrate
> the array… (Nor did we measure how well it was calibrated out-of-the-box.).

Does the 'nor' mean you did _not_ calibrate it ?

> I don’t actually think that there are any special requirements.

There are.

The required gain (at LF) means that small differences in capsule
sensitivity are amplified as well, and this distorts the resulting
polar pattern. 

The simplest possible example would be a first order component X
being produced from the difference of two omni capsule signals
A and B, so

  X = (A - B) * (1 + j (F0 / F))

where F0 will depend on the distance between the capsules.

Now if A has actually 1 dB more gain the difference signal becomes

  1.12 * A - B = (A - B) + (0.12 * A)

The second term, amplified by the filter for low F, will add
an omni component to X. 

So the maximum gain that can be used depends not only on how
much noise can be tolerated, but also on the calibration 
accuracy (and long term stability) of the capsule gains.


Ciao,

-- 
FA




 


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Re: [Sursound] A 7th-order array with 16 microphones

[Jens Ahrens]

Hi Marc,

Yes, as with SMAs, the aliasing frequency scales inversely with the radius.

But a small radius limits the low-frequency end: The smaller the radius is, the 
higher will be the frequencies above which a certain (higher) order can be 
deduced. The 0th order is always there. For an array with a very small radius 
the 1st order may only be available above a certain frequency (and up until the 
aliasing frequency) etc.

The radius of this particular prototype had a very different motivation:

We figured out that there existed only about half a dozen arrays in the world 
that use this equatorial layout, and all of them were experimental prototypes. 
The one that we used in the video was originally built for motion-tracked 
binaural where the array needs to have a radius similar to that of a human head 
so that a useful ITD is produced. Here are the details of the array: 
https://www2.ak.tu-berlin.de/~akgroup/ak_pub/abschlussarbeiten/2018/Fiedler_MasA.pdf
  Fortunately, this is indeed a size that allows for fitting all hardware into 
the scattering body.

It is certainly no coincidence that this same size works well also for SMAs 
that perform spherical harmonic decomposition for subsequent binaural 
rendering. Many authors concluded this. One author that I can remember off the 
top of my head is Benjamin Bernschütz. His PhD thesis contains a lot of 
information on this.

If it works well for SMAs, then it works well for EMAs!

It was indeed a bit of luck that we were able to get hold of a prototype that 
was ideal for our purposes. In the near future, we will look into how small the 
array can be before things break down.

Best regards,
Jens



On 1 Dec 2021, at 15:55, Marc Lavallée 
mailto:m...@hacklava.net>> wrote:

Le 2021-12-01 à 09 h 20, Jens Ahrens a écrit :
I’m not sure if I understand your question correctly. I’ll do my best to be 
comprehensive so that my response covers what you are interested in:

For this type of array, the spatial aliasing frequency f_a is dependent on 
order N and radius R of the array in the exact same manner like with spherical 
microphone arrays (SMAs): N = (2 pi f_a / c) R

   N = 7
   R = 0.0875 m

So that

   f_a = 4.3 kHz

With a  bit of algebra, f_a = c  N / ( R 2 pi ).
So a smaller radius for the sphere would improve f_a?
Was 0.0875 m chosen in order to embed some hardware?

Marc
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Re: [Sursound] A 7th-order array with 16 microphones

[Marc Lavallée]

Le 2021-12-01 à 09 h 20, Jens Ahrens a écrit :

I’m not sure if I understand your question correctly. I’ll do my best to be 
comprehensive so that my response covers what you are interested in:

For this type of array, the spatial aliasing frequency f_a is dependent on 
order N and radius R of the array in the exact same manner like with spherical 
microphone arrays (SMAs): N = (2 pi f_a / c) R

N = 7
R = 0.0875 m

So that

f_a = 4.3 kHz


With a  bit of algebra, f_a = c  N / ( R 2 pi ).
So a smaller radius for the sphere would improve f_a?
Was 0.0875 m chosen in order to embed some hardware?

Marc
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Re: [Sursound] A 7th-order array with 16 microphones

[Jens Ahrens]

Hi Fons,

I’m not sure if I understand your question correctly. I’ll do my best to be 
comprehensive so that my response covers what you are interested in:

For this type of array, the spatial aliasing frequency f_a is dependent on 
order N and radius R of the array in the exact same manner like with spherical 
microphone arrays (SMAs): N = (2 pi f_a / c) R

   N = 7
   R = 0.0875 m

So that

   f_a = 4.3 kHz

The lower end is limited by the radial filter gain that the user chooses. The 
radial filters are not the same like with SMAs, but they are very similar so 
that the limitations are the same. 

   0th and 1st order are available for all frequencies. 
   2nd order approx. above 200 Hz
   3rd order approx. above 500 Hz 
   etc.

I cannot comment on calibration requirements because we did calibrate the 
array… (Nor did we measure how well it was calibrated out-of-the-box.). I don’t 
actually think that there are any special requirements. As before, much of the 
physical limitations are qualitatively (and also quantitively) similar to SMAs. 

Best regards,
Jens




> On 1 Dec 2021, at 12:36, Fons Adriaensen  wrote:
> 
> On Wed, Dec 01, 2021 at 09:03:59AM +, Jens Ahrens wrote:
> 
>> Their main advantage over conventional spherical microphone arraysi
>> is the fact that they require only 2N+1 microphones for Nth spherical
>> harmonic order
> 
> For the microphone in the video, what is the usable frequency range
> for each order, taking into account required gain and calibration
> accuracy (for LF) and aliasing (for HF) ?
> 
> Ciao,
> 
> -- 
> FA
> 
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Re: [Sursound] A 7th-order array with 16 microphones

[Fons Adriaensen]

On Wed, Dec 01, 2021 at 09:03:59AM +, Jens Ahrens wrote:
 
> Their main advantage over conventional spherical microphone arraysi
> is the fact that they require only 2N+1 microphones for Nth spherical
> harmonic order

For the microphone in the video, what is the usable frequency range
for each order, taking into account required gain and calibration
accuracy (for LF) and aliasing (for HF) ?

Ciao,

-- 
FA

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