Cross Correlation and Noise Reduction in Mic Arrays

Bob Cain wrote:
...
> Among the numerous capsules the self noise of each would be
> independant and uncorrelated.  The signals, on the other
> hand, would be highly correlated.  There will be some time
> of arrival differences in the sound pickup but little
> magnitude differences.

My first take on this problem would be to "standardize" each sensor
output (ie. compensate known differences of the frequency response,
phase, delay, etc. between the sensors). For each sensor you get a
response h_k (k in 1 .. N, where N is the number of sensors). You
basically just need to find the relative response with respect to any
one reference sensor that you can define arbitrarily. If you know the
placement, the direction and frequency response of the sensors, this
should theoretically pose no problem (I can imagine that this could
lead to problems in practice).

If s_k is the output of the k-th sensor, and s_k' = h_k * s_k  (*
denotes convolution with the compensation filter h_k) the compensated
output of each sensor, then a first estimate of the "true" signal (that
is the signal "seen" through the reference sensor) is the average r =
1/N (s_1'+...+s_N'). An estimate for the denoised signal would be s_k''
= (h_k)^-1 * r, the deconvolution of the average.

You could refine the estimate r by weighting each s_k with an
additional weighting filter w_k which could define the amount of
information that sensor k contributes to the average signal. Some
non-linear weighting function could lead to a more robust estimate (for
examle if a sensor is defect).

This would be my first naive approach. Howerver, I should think the
problem of estimating a signal from many sensor outputs is a well
studied problem. I don't know the technical term though.

Regards,
Andor

On Sat, 09 Apr 2005 20:01:39 -0700, Bob Cain
<arcane@arcanemethods.com> wrote:

> Look at:
>
>    http://www.atvs.diac.upm.es/publicaciones/docs/Bot00a.pdf

OK, I've looked, and, as usual, it's mostly over my head, but
doesn't this apply to external "noise", meaning anything
unwanted, rather than internal noise, meaning something
subject to the Second Law?

If so, it would seem to be within the murky purview of room
de-convolving that you (*don't*) hint at so often. Large area
receivers imply directionality. More is more, etc.

Something the size of a human head has good directionality
above one and a half kiloHertz or so...   Add time-sensitive
selective sensing around the surface...

Sounds like a very interesting project. Good fortune,

Chris Hornbeck
6x9=42 April 29