[Sursound] reinvention of the wheel??

2013-04-20 Thread Dave Malham
Just received an email which - seems someone else is reinventing the
Soundfield again - see http://www.quaud.io/
This time it's based on mems microphones and is very small so it ends up
using blind source separation in order to get good source-interference
ratios. There's only one reference to Gerzon and Craven in their papers,
the latest one, and it's only brief - and no mention at all of Villa
Pulkki's work which seems closely related. Interesting...

Dave

-- 
As of 1st October 2012, I have retired from the University, so this
disclaimer is redundant


These are my own views and may or may not be shared by my employer

Dave Malham
Ex-Music Research Centre
Department of Music
The University of York
Heslington
York YO10 5DD
UK

'Ambisonics - Component Imaging for Audio'
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Re: [Sursound] Optimised Decoder matrix (Ambdec)

2013-04-20 Thread Dave Malham
I agree with Fons here. We have used essentially this approach when we
needed to play back Ambisonic material on The Morning Line (which is very
irregular and needs preferably to use VBAP) right from when we first set it
up back in 2008 and you definitely won't find it easy to get it work
optimally - manual tweaking is pretty well always needed. However, at this
stage, there probably isn't a better approach for low order Ambisonics,
either automatic or manual.

  Dave

On 19 April 2013 23:33, Fons Adriaensen  wrote:

> On Fri, Apr 19, 2013 at 10:12:20AM -0700, Aaron Heller wrote:
>
> > F. Kaiser, “A Hybrid Approach for Three-Dimensional Sound
> Spatialization,”
> > Algorithmen in Akustik und Computermusik 2, SE, May 2011.
> >
> http://iaem.at/kurse/winter-10-11/aac02se/2011_Kaiser_SeminararbeitVersatileAmbisonicDecoder.pdf
> >
> >
> > The toolkit reads speaker locations from CSV files (and other formats,
> > including ambdec presets) and writes out presets files for Fons' Amdec
> > decoder.  There's also an initial implementation of a Faust backend, that
> > produces decoders that can be compiled to VST, Supercollider, Pd, MaxDSP,
> > ...(see http://faust.grame.fr/ for more about Faust).
> >
> > AllRAD is a hybrid ambisonic/vbap technique, especially suited to
> irregular
> > arrays.   The idea is you design a decoder for a regular array (in this
> > case a 240 virtual speaker spherical design) and then map those signals
> to
> > the real array using Pulkki's VBAP.
>
> This is one of the many methods I tested, and rejected. If applied
> 'blindly' it can easily produce rather suboptimal results (*) - as
> would any method that in the end amounts to linear combinations of
> the outputs of a 'regular layout' decoder. Things improve if the
> VBAP gains are adjusted manually, but that more or less defeats the
> purpose of an 'automatic' method, and even results obtained that way
> are suboptimal.
>
> The problem behind this that adding VBAP (or any other) pannings of
> (partially) correlated signals will not produce the correct result
> - at least not in the frequency range where rE magnitude and direction
> are the metrics. There are solutions to this, but they are not simple.
>
> Ciao,
>
>
> (*) Try for example a 5th order horizontal decode to a regular ring
> of 12 speakers, then remove one of them and it replace by a VBAP
> panning into the two nearest ones.
>
>
> --
> 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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>



-- 
As of 1st October 2012, I have retired from the University, so this
disclaimer is redundant


These are my own views and may or may not be shared by my employer

Dave Malham
Ex-Music Research Centre
Department of Music
The University of York
Heslington
York YO10 5DD
UK

'Ambisonics - Component Imaging for Audio'
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[Sursound] Re-re-inventing the wheel

2013-04-20 Thread Eric Carmichel
Just received an email which - seems someone else is reinventing the Soundfield 
again - see http://www.quaud.io/
This time it's based on mems microphones and is very small so it ends up using 
blind source separation in order to get good source-interference ratios. 
There's only one reference to Gerzon and Craven in their papers, the latest 
one, and it's only brief - and no mention at all of Villa Pulkki's work which 
seems closely related. Interesting...
Dave

Hi Dave,
That is interesting... but then, too much info might preclude their getting a 
patent? I did notice that the mic in question uses omnidirectional capsules. 
I'll have to re-re-read the literature by Gerzon, Craven, et al. I recall that 
Gerzon's earliest ideas depended on figure-of-eight mics (akin to Blumlein 
Stereo), whereas all later incarnations use subcardiod mics. Whether this is of 
any consequence or not... I don't know. Does beam forming or delay techniques 
to create additional first-order patterns from the omnidirectional mics change 
up the design (and math) from arrays using intrinsically cardiod mic elements? 
Anyway, I certainly hope credit will go to where credit belongs. Long live 
Ambisonics!
Eric C.
PS--I look forward to listening to the YouTube samples of from the 
aforementioned link. I hope it's not another helicopter. Or worse, a barber 
shop scenario.
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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread David Pickett

At 11:24 20-04-13, Eric Carmichel wrote:
>Just received an email which - seems someone else is reinventing the
>Soundfield again - see http://www.quaud.io/
>This time it's based on mems microphones and is very small so it ends
>up using blind source separation in order to get good
>source-interference ratios. There's only one reference to Gerzon and
>Craven in their papers, the latest one, and it's only brief - and no
>mention at all of Villa Pulkki's work which seems closely related.
>Interesting...
>Dave
>
>Hi Dave,
>That is interesting... but then, too much info might preclude their
>getting a patent? I did notice that the mic in question uses
>omnidirectional capsules. I'll have to re-re-read the literature by
>Gerzon, Craven, et al. I recall that Gerzon's earliest ideas depended
>on figure-of-eight mics (akin to Blumlein Stereo), whereas all later
>incarnations use subcardiod mics.

If one regards the subcardioid as made up of omni and figure of eight 
components, is it not the case that the ambisonic XYZ signals of the 
Soundfield Mic are derived solely from the figure of eight components?


Further, if this new mic relies on omni capsules, how will it not 
suffer from the signal to noise ratio problem of Blumlein's method of 
deriving stereo from two omnis?


David

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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread Eric Carmichel

SNR wouldn't have been my initial concern because I have some wee-tiny 
electrets that have (purportedly) +10 dBA noise--pretty low for a small 
capsule.
When I think of the "classic" multi-polar mics such as the 
AKG-414, the multiple patterns are often derivatives of back-to-back 
diaphragms sharing a common stator (I think... not a mic expert here). 
In comparison, ribbon mics (Coles, Royer, vintage RCA, etc.) are 
figure-of-eight (or bi-directional) because of their pressure-gradient 
design. Cardiod condenser and dynamic mics have rear venting for 
delay/cancellation (delay using materials of varying density, not merely
 time-in-air delay), hence their directional characteristics. So...
Having
 directional characteristics provides direction-dependent output levels 
for each of four mics. Spacing, of course, provides a time
 difference component for computing direction. The ideal is no 
inter-capsule spacing (= zero time delay). Tightly spaced omnis are just
 that... omni... and wouldn't have discernible time or level differences
 unless there's *some* time difference or pressure difference. Sound 
intensity probes rely on a phase (and level) difference to determine the
 vector quantity of sound power (SPL alone being a scalar quantity).
So,
 based on acoustical signal processing and beam forming described by, 
for example, Vorlander, I was curious whether the *new* surround mic 
used such processing to create four virtual subcardiods that would also 
serve as the equivalent *A-format* mics. Any single mic, or average of 
all mics, would be the omni component.
For mics such as the AKG 414, 
the electrically and acoustically combined response yields one polar. 
So, I was really wondering how four omni mics could provide unique info 
for multiple directions. A highly-directional mic
 can be created using omnis and beam forming, but not a *series* of 
directions at a given instant. Now, scratching my head, there's no 
reason that multiplexing among the mics couldn't be used to create 
rapidly-changing patterns that are akin to interleaved quad channels. 
That is to say, only one direction is picked up at a time, but the 
derived direction changes swiftly enough that it appears to have four 
*directional* mics (is this a new idea... it just came off the top of my
 head... most of what I think up has been done.)
I just found the 
technology interesting/curious, and wondered where it might deviate from
 the Soundfield mic to the point of being a unique design. One aspect of
 a patent is that the invention be unique.

Above post in response to:: If one regards the subcardioid as made up of omni 
and figure of 
eight components, is it not the case that the ambisonic XYZ signals of 
the Soundfield Mic are derived solely from the figure of eight 
components?

Further, if this new mic relies on omni capsules, how
 will it not suffer from the signal to noise ratio problem of Blumlein's
 method of deriving stereo from two omnis?

David
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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread Sampo Syreeni

On 2013-04-20, Eric Carmichel wrote:

Does beam forming or delay techniques to create additional first-order 
patterns from the omnidirectional mics change up the design (and math) 
from arrays using intrinsically cardiod mic elements?


Not per se, as we can see from designs like the Eigenmike. However, it 
does lead to hugely wasteful use of microphones compared to letting 
physics do the basic job of discriminating between waves going in 
opposite directions.


Especially so since there's a topological problem with extended arrays 
which aren't internally sampled to the spatial aliasing limit. (I think 
it was Filippo who first raised this one.) If you think about a 
spherical array of omnis on the one hand and omnis mounted on a sphere 
(or cardioids) on the other, the latter has a topological hole in the 
center whereas the former does not. The sphere of directions has that 
hole too, so if you forget about W for a second, those holes 
topologically have to map to each other when going from the array 
signals to the spherical harmonic representation (finite dimensional 
linear maps are continuous, so they preserve holes). That means that 
your A-format to B-format transform will necessarily end up mimicing 
that singularity, and that's expensive in mic terms. (As a whole, the 
hole ain't there because once you add W, it kind of patches over it. But 
that doesn't much help you when you consider the derivation of each 1+ 
order signal in isolation.)


The nasty side effect of that is that knowing the field over a sphere 
doesn't uniquely determine the field inside the sphere, whereas knowing 
the field and that there's a rigid ball in the center (the singularity, 
the hole) in addition does get you there. The same goes for knowing both 
the pressure field and its normal velocity, or knowing the outwards 
pointing cardioid response, because in both cases you can easily 
synthesize the singularity. If you only work with monopoles in the free 
field, eventually you'll end up simulating the dipole (velocity) 
component, at the cost of extra mics, plus spatial aliasing concerns 
force you to oversample in space. Effectively you have to go look inside 
the sphere in order to fully determine the field there, whereas it would 
have been enough to look just at the border if there was some physical 
mechanism which gained direct access to the velocity component of the 
field, like an obstruction giving rise to a cardioid response, a genuine 
velocity measurement like a MicroFlown, or that rigid sphere in the 
center which mixes pressures and velocities by imposing a boundary 
condition of zero normal velocity.


Okay, that's almost abstract nonsense and it took ages for me to grasp 
what was going on, so let's look at it from another perspective. How 
could two fields with the same boundary pressure field happen? The 
secret is a special kind of standing wave with full spherical symmetry. 
If you have that, you can place one of the antinodes (a full sphere) 
right at your microphone rig boundary. If the mics are monopoles, they 
won't sense the field at all, so that means any field with this property 
can be freely added to any other field without the A-format changing. If 
you had access to normal velocity as well, all of the information would 
be there, but if you only have pressure sensitive monopoles, you'll 
necessarily have to place some of them inside the sphere to tell the 
difference. And if you think about it, that special field is not just a 
harmless corner case: it's composed of all the modes of a spherical 
cavity under the boundary constraint of zero pressure (plus a matching, 
uniquely determined field outside the sphere); if you want to tame them 
all, you pretty much have to sample the whole interior to some highish 
spatial frequency limit.


The same can't happen once you put a singularity in the middle, which is 
what outwards pointing cardioids too end up doing. Then the remaining 
modes are topologically speaking those of a sphere, not those of a ball, 
and monopoles suffice to capture them. I'm also pretty sure this is 
connected to some nasty algebraic weirdness (spin groups as double 
covers of their orthogonal counterparts) through the NFC-HOA papers, 
because in the latter the sphere of directions is covered twice with not 
only an incoming but also an outgoing field (cardioids pick one, a full 
Kirchhoff-Helmholtz integral can represent both) which too patches the 
hole. Dunno how the details might work out, though.

--
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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread Sampo Syreeni

On 2013-04-20, David Pickett wrote:

If one regards the subcardioid as made up of omni and figure of eight 
components, is it not the case that the ambisonic XYZ signals of the 
Soundfield Mic are derived solely from the figure of eight components?


Not quite, because at high frequencies the mics aren't exactly 
coincident, so that the following A-to-B matrix derives some of W from 
the fig-8 (or velocity) components and some of XYZ from the monopole 
contributions. But almost: XYZ are conceptually just three fully 
coincident fig-8's, sensitive purely to velocity (and derivable in this 
case from pressure gradient over time).


Further, if this new mic relies on omni capsules, how will it not 
suffer from the signal to noise ratio problem of Blumlein's method of 
deriving stereo from two omnis?


It most likely does, or it has to compensate with an extended array of 
omnis, adding to cost.

--
Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front
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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread David Pickett

At 15:27 20-04-13, Sampo Syreeni wrote:

If one regards the subcardioid as made up of omni and figure of 
eight components, is it not the case that the ambisonic XYZ signals 
of the Soundfield Mic are derived solely from the figure of eight components?


Not quite, because at high frequencies the mics aren't exactly 
coincident, so that the following A-to-B matrix derives some of W 
from the fig-8 (or velocity) components and some of XYZ from the 
monopole contributions. But almost: XYZ are conceptually just three 
fully coincident fig-8's, sensitive purely to velocity (and 
derivable in this case from pressure gradient over time).


But... How close to the theoretical A format polar diagramy are the 
XYZ components of the Soundfield (or Tetramic) microphone at 
frequencies above those at which they are essentially coincident?


At 15:08 20-04-13, Eric Carmichel wrote:

>SNR wouldn't have been my initial concern because I have some wee-tiny
>electrets that have (purportedly) +10 dBA noise--pretty low for a small
>capsule.

Granted this is better than the mics that Blumlein could command, but 
when it comes to the processing of the raw outputs, is not the 
problem of lower level signals produced by subtraction still a real one?


David

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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread Sampo Syreeni

On 2013-04-20, David Pickett wrote:

But... How close to the theoretical A format polar diagramy are the 
XYZ components of the Soundfield (or Tetramic) microphone at 
frequencies above those at which they are essentially coincident?


Rather far from them, because the ideal A format response is a) a 
mixture of pressure and velocity and b) not even a 1-1 mix for a 
cardioid. However, they are essentially perfect representations of the 
true XYZ velocities (ideal B-format) to about 10kHz, where the 3.3cm 
wavelength approaches the mic diameter. So, pretty darn good, 
considering, and even beyond that at least the intensity response stays 
controlled. Well implemented the classical tetrahedral design is an 
outstanding realization of the theory.

--
Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front
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Re: [Sursound] reinvention of the wheel??

2013-04-20 Thread Martin Leese
Dave Malham wrote:

> Just received an email which - seems someone else is reinventing the
> Soundfield again - see http://www.quaud.io/
> This time it's based on mems microphones and is very small so it ends up
> using blind source separation in order to get good source-interference
> ratios. There's only one reference to Gerzon and Craven in their papers,
> the latest one, and it's only brief - and no mention at all of Villa
> Pulkki's work which seems closely related. Interesting...

See also their US Patent Application
20110015924, ACOUSTIC SOURCE SEPARATION

http://appft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PG01&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.html&r=1&f=G&l=50&s1=%2220110015924%22.PGNR.&OS=DN/20110015924&RS=DN/20110015924

This was the only US Patent or US Patent
Application that I could find by this team.

Regards,
Martin
-- 
Martin J Leese
E-mail: martin.leese  stanfordalumni.org
Web: http://members.tripod.com/martin_leese/
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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread Eric Carmichel
I truly appreciate your informative and highly detailed response. For 
helping understand spherical harmonics (or Legendre polynomials?), and 
for mics lying on surface of a sphere, this helps a lot.

But here's what
 I don't understand about the quaud (quaud.io) mic: They say the four 
omnidirectional mics lie on the corners of a tetrahedron--essentially 
same arrangement as Soundfield, but with omni mics and 
positioned on corners of tetrahedron. Re mics on a sphere: In a corner-oriented 
tetrahedral arrangement, the mics would lie on a *virtual* sphere just as much 
as mics on a sphere could be lying on a virtual tetrahedron. But at some point 
the actual (physical) surface becomes a piece of the whole. This is clearly 
evident when the sphere is large enough to be a human head. So I'm not always 
clear as to whether it's the mics' virtual orientation in space, or the 
physical boundary of a spherical surface, that *shapes* the sound and creates 
the requisite time and pressure differentials.
Dave M's original post states that someone else is... again... re-inventing the 
Soundfield mic. I'm sure that I'm not the only person who is curious as to what 
makes the quaud (Trademark) mic *unique* and different from the Soundfield 
mic--particularly if the quaud mic is patented. Is, for example, more than one 
tetrahedral arrangement used to achieve *surround* spacing--which would then
 be a wholly different thing? I need to read further. Thanks again for 
info. The following was cut-and-pasted from their website (I think Dave 
provided all of this in his post, too):

quaudio
 comprises four omnidirectional microphones located at or near to the 
corners of a regular tetrahedron. Since these capsules are
 omnidirectional they can be located at the opposite corners of a cube 
with no loss in generality. This arrangement is straightforward to 
achieve in a standard PCB assembly line by soldering two pairs of MEMS 
or electret capsules on opposite sides of the substrate. Alternatively 
it is possible to solder three capsules to one side and a single capsule
 to the other. In both cases the acoustic centre of each sensor should 
be separated laterally by a distance corresponding to the vertical 
separation between membranes on either side of the device
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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread Fons Adriaensen
On Sat, Apr 20, 2013 at 01:08:57PM -0700, Eric Carmichel wrote:

> A highly-directional mic can be created using omnis and beam
> forming, but not a *series* of directions at a given instant.

??? What would stop anyone from using whatever beamforming 
algorithm twice (or more times) in parallel, using the same
mic signals as input ?

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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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread Fons Adriaensen
On Sat, Apr 20, 2013 at 03:49:22PM -0500, David Pickett wrote:

> Granted this is better than the mics that Blumlein could command,
> but when it comes to the processing of the raw outputs, is not the
> problem of lower level signals produced by subtraction still a real
> one?

It certainly is. The problem is not just noise, but also gain
calibration and stability.

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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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread Fons Adriaensen
On Sat, Apr 20, 2013 at 02:38:42PM -0700, Eric Carmichel wrote:

> So I'm not always clear as to whether it's the mics' virtual
> orientation in space, or the physical boundary of a spherical
> surface, that *shapes* the sound and creates the requisite time
> and pressure differentials.

Omni mics don't have any orientation, so its only the pyhsical
shape they are mounted on that would create directivity and
time differences.

For a 'classic' soundfield mic it is mostly the mic's polar
pattern that leads to differences between the A-format signals,
except at HF where the physical size and shape of the array
comes into play (which is an unwanted thing in this case).

Regarding Quaudio there is some confusion (or obfuscation) going
on as two things get mixed up: the mic (which apart from its small
size is not really anything new), and the processing used to 
separate sources (which has some novel elements). 

Regarding the latter, in the papers it is stated that the same
algorithm can be used with a standard tetrahedral mic - the 
required input is B-format. The separation method proposed seems
to rely on long-term statistics of the intensity vector, which 
would mean it can't be used for e.g. moving sources. The test
cases documented are for one, two or three static sources.

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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Re: [Sursound] Re-re-inventing the wheel

2013-04-20 Thread Sampo Syreeni

On 2013-04-20, Eric Carmichel wrote:

But here's what I don't understand about the quaud (quaud.io) mic: 
They say the four omnidirectional mics lie on the corners of a 
tetrahedron--essentially same arrangement as Soundfield, but with omni 
mics and positioned on corners of tetrahedron.


For a near-coincident array this is not such a problem, because if you 
think about the modes which might fit within it, they happen at such 
high frequencies (above 10kHz) that we can largely neglect them. In this 
very special first order only case, you can approximate three pressure 
gradients (and by filtering them, velocities XYZ) and an average 
pressure (W) using for monopoles as well. In this case the mic itself is 
the singularity and the physics doing the heavy lifting is the fact that 
soundfields do have four independent degrees of freedom even pointwise; 
the first four ambisonic components are present even in a point, and 
even if you approximate the directional ones by differences of 
monopoles, you can get the job done. In the theoretical sense the price 
you pay is reduced sensitivity at low frequencies, which leads to noise 
amplification when you do the differencing. Practically the mic assembly 
itself is a physical barrier which gives you some leverage -- and in 
this case they're actually talking about mounting the whole thing on the 
surface of a PCB too. The trouble with inwards and outwards propagation 
goes away because there is no inside in a coincident array.


So, the mic itself is nothing new, just yet another realization of a 
soundfield mic, quite possibly cheaper but also less sensitive at LF due 
to size. The real contribution appears to be in the source separation 
algorithm.


For that they do an intensity analysis in the Fourier domain much like 
DirAC does. Then they apply a sizable bank of beam forming filters in 
all directions under a planewave assumption, which is one way to do 
infinite order decoding (in older forms called steering, or a nonlinear, 
dynamic matrix). Finally instead of picking one of the beamformers per 
source they do a principal component reduction and pick the leading 
eigenterms. The combination of the last two steps is essentially 
equivalent to just doing nonorthogonal factor analysis of the 
instantaneous directions of arrival we got from the real (propagating, 
nonreactive) part of thefirst step, except that the second step helps us 
avoid a number of basis selection problems (or permutation problems as 
the authors call them) so that coherent sources stay together.


That sort of stuff always works as long as the problem is at most 
complete, which is why with four mics they never try to go beyond three 
or four sources. Any extra sources -- from reflections and the like -- 
will end up being distributed into the derived signals based on the 
eventual virtual mic patters. In this kind of a system those patterns 
are then pretty haphazard in that while they yield maximum response 
towards each of the first four estimated sources (arbitrary 
directionality) and each pattern gets a null in the direction of the 
other three, in between the directions there is zero control of sidelobe 
direction (its maxima are somewhere in the direction of the reciprocal 
overcomplete "basis", i.e. highly unpredictable if the sources deviate 
from tetrahedral placement) or amplification. In general that sort of 
thing probably shouldn't be analysed in the spherical framework in the 
first place, but simply as a MIMO beamforming problem with rigid spacing 
of nulls. Such things yield optimal separation of direct sound, but in a 
busy space they can royally mess up reverb and especially any attempts 
at recombination of the derived signals (there's frequency selectivity 
and maybe phase stuff going on here as well, so in that sense similar to 
SRS's to-5/7.1 upconversion stuff, which I wouldn't easily use in a 
studio environment but at most as an active matrix).


This is clearly evident when the sphere is large enough to be a human 
head. So I'm not always clear as to whether it's the mics' virtual 
orientation in space, or the physical boundary of a spherical surface, 
that *shapes* the sound and creates the requisite time and pressure 
differentials.


Omnis obviously don't have any directionality. Cardioids (and most 
fig-8's) derive their directionality (i.e the mixing stuff) from their 
physical design, which has a boundary, with its boundary conditions, 
somewhere. E.g. the capsules used in a SoundField carry their own "wall" 
with them. MicroFlowns and the like are the exception because they touch 
velocity directly.

--
Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front
+358-50-5756111, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
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