# Simulating a sound field and two mics (Pradyumna S Upadrashta )

```Subject: Simulating a sound field and two mics
Date:    Thu, 17 Apr 2003 09:51:00 -0500

Dear Ki-Young,

Simulating your situation is straightforward. It is essentially the
"forward problem" -- that is, you define a linear mixing matrix and
proceed to write out the linear model that describes the activity at
each microphone, given a specific source distribution.

I'm more familiar with "forward" (you provide the geometry) and
"inverse" (no solutions without making assumptions) problems in EEG /
MEG analysis.

Say Vout(i) is the voltage measured at your microphone, i, then you can
write the forward model as:

Vout(i) = G1(i)*Y1 + G2(i)*Y2 + ... + Gn(i)*Yn + error

Where G1, G2, G3,...,Gn are the individual "mixing matrices" for each
source Yk, with n sources total.

Vout(1) is the output measured at mic 1
Vout(2) is the output measured at mic 2

All you need now is a reasonable approximation of the geometry of your
scenario, which will determine the elements of the Gk's. It will have to
account for loss as a function of distance and medium. Presumably this
is constant for a given geometry, which is what allows us to write the
linear equation above; i.e., the loss w.r.t. distance is nonlinear since
sound amplitude should fall off as r^2; i.e., sound generically
propagates with a spherical wavefront and is described by
compression/rarefaction or longitudinal propagation. Of course the
situation is complex for different types of sound sources; for a good
overview, look at the following:

The Yk are the activity (amplitudes) of the sources over time, i.e., a
time-series of the amplitudes generated by the sources.

The "error" term accounts for spurious background noises in the
environment (e.g., air flow around the mic head, spurious noises ala
60Hz electrical frequencies, etc.). Measurement of the output of a
single/double microphone in a "silent" room might be a good
approximation of this term.

Hope that helps. Or at least, hope it doesn't confuse ;-)
I might have missed something since I did this rather quickly.

__________________________________
612-725-2000 x 1464

>----- Original Message -----
>From: "Ki-Young Park" <pkyoung(at)EEINFO.KAIST.AC.KR>
>To: <AUDITORY(at)LISTS.MCGILL.CA>
>Sent: 13 April 2003 17:23
>Subject: correlation btw 2 singals incoming two ears from
>distributed souces
>
>
>> Dear all,
>>
>> I am working on the speech stuff, recognition and enhancement. While
>> using two signals with two microphones moderate distance
>apart, say a
>> few tens of centimeters. I assume there is one speech source,
>> and distributed noise sources all around a room
>> instead of a point-source.
>> ( and also assume additive noise. )
>>
>> Is there publication on the correlation of two signals incoming into
>> two mics, when there are distributed noise sources around.
>>
>> and is there any way to simulate this situation?
>>
>> Any comments and references will be appreciated.
>>
>> Thank you.
>>
>>
>
>------------------------------
>
>End of AUDITORY Digest - 15 Apr 2003 to 16 Apr 2003 (#2003-84)
>**************************************************************
>
```

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Electrical Engineering Dept., Columbia University