Re: Blind Source Separation by Sparse Decomposition ("Richard J. Fabbri" )

Subject: Re: Blind Source Separation by Sparse Decomposition
From:    "Richard J. Fabbri"  <fabbri(at)NETAXIS.COM>
Date:    Tue, 7 Sep 1999 10:58:28 -0400

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" (at) the usual GND and +VS ends of the supply voltage. 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. Regards, 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(at) | >> | 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) | >> | | >> ------------------------------------------------------------------------

This message came from the mail archive
maintained by:
DAn Ellis <>
Electrical Engineering Dept., Columbia University