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Re: Blind Source Separation by Sparse Decomposition

Dear Michael,

Thanks for your response about the number of receivers versus the number
of sources It makes the human ability to (imperfectly) deal with many
sources with only 2 ears even more intriguing.  Somehow humans are trading
off perfection in a narrow set of circumstances for flexibility.  I
suspect _heuristic_ approaches to CASA (computational auditory scene
analysis) would work more like people do.

Here is why I asked about the clipping problem.  I'm no physicist so I
can't give you an exact physical formulation of the problem.  However, it
seems to me that clipping destroys the linear additivity of the frequency
components in the signal.  Here is a simple example: mix a low amplitude
high frequency component with a high amplitude, low frequency one.  In the
waveform, the high frequency seems to be riding on top of the low
frequency at all points in the signal.  Now clip the signal.  Now the high
frequency signal is missing in the segments that exceed the clipping
threshold.  It could have changed in frequency (and then back again) for
all we know.

I wanted to know whether, by destroying the additivity of the signals,
clipping ruled out any mathematical methods for separation that are based
on this additivity.  I'm also not sure what echos and reverberation would
do to such mathematical methods.

- Al
On Mon, 6 Sep 1999, Zibulevsky Michael wrote:

> Al,
> You wrote:
> > - How many receivers of the signal would it require to segregate 4
> > sources?  Is there any fixed relation between the number of receivers
> > required and the number of underlying signals in the mixture?
> in general you need less sensors, than sources (say, 2 or 3 sensors for
> 4 sources), but it leads you to the  computationaly difficult and not
> very stable procedure). So, if you have a choice, it would be better to
> have
> the  number of sensors at least the same as the number of sources.
> You wrote:
> > - What would happen if the signal were clipped at some arbitrary
> > amplitude?
> It's an interesting question. I never heard, that somebody was solving
> such a problem, but there might be in principle few possibilities to
> treat it. Could you say a bit more about the physics of this problem?
>   --Michael
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> | Michael Zibulevsky, Ph.D.             Email: michael@cs.unm.edu      |
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