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Re: Blind Source Separation by Sparse Decomposition

Al, Michael -

"The physics of the problem" as Michael called it, require, first, a
model through which to pass ("clipped") signals and, later,
inspect the resultant Source data.

However, without first proposing that model, and, in an effort to
promote dialogue, I propose a somewhat more severe form of
clipping, i.e., high gain amplification (a voltage comparator) that
conveniently "clips" @ the usual GND and +VS ends of the supply

In this extreme clipping case the only thing remaining of the original
audio are the zero-crossings and, a very high speed (usually nsec)
has been introduced at the zero-crossing transitions.  Yet, upon
audition we perceive intelligible speech under these circumstances.
And, in the spirit of Al's comments, all frequency components other
than those related to zero-crossings have been removed.

Returning to the specific question of Source "segregation", it would
be interesting to experiment with binaural recordings by clipping the
Left/Right audio with voltage comparators before passing the L/R
channels to the usual "stereo" headset for binaural audition.

Again, as per Al's comment, "...the human ability to (imperfectly) deal
with many sources with only 2 ears [is] even more intriguing."

Anyone who tries this proposed, severe (binaural) clipping will be
further intrigued by our 2 ear processing abilities.

Of course, an A/B audio switch should also be employed so as to
allow a ready way to compare the original binaural sound to the
clipped sound.

Given the non-commercial nature of this forum, I would not initially
supply the web addresses of binaural cassettes recordings but, if
asked, would privately supply a website I've found useful.

Rich Fabbri
Scarce Ideas
____________________Reply Separator__________________
>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
>> ------------------------------------------------------------------------
>> | Michael Zibulevsky, Ph.D.             Email: michael@cs.unm.edu      |
>> | Brain Computation Laboratory          Phone: 505/265-6448 (home)     |
>> | Computer Science Dept., FEC 313              505/265-5313 (home)     |
>> | University of New Mexico                     505/277-9426 (work)     |
>> | Albuquerque, NM  87131  USA           FAX:   505/277-6927 (shared)   |
>> |                 http://iew3.technion.ac.il:8080/~mcib/               |
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