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From: ashok@atrp.mit.edu (Ashok C. Popat)
Newsgroups: comp.dsp
Subject: square root and inverse filter questions
Message-ID: <1990Sep6.114934.217@athena.mit.edu>
Date: 6 Sep 90 11:49:34 GMT
Sender: daemon@athena.mit.edu (Mr Background)
Organization: Massachvsetts Institvte of Technology
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Two questions about filters:

Suppose I have a filter with impulse response h(n), having
nonzero values only in the range 0 <= n <= N-1.

I am interested in finding:

  (1)  An approximate "square root" of this filter, in the convolution
       sense.  That is, I am looking for a filter with impulse response
       f(n), which, when convolved with itself, approximates h(n).  In my
       application, this filter need not be FIR, nor must it have a
       rational system function, but it must be stable and have negligible
       energy far away from the origin.

  (2)  An approximate FIR inverse of the filter.  That is, I am looking
       for a filter with finite-extent impulse response g(n) such that
       g(n) convolved with h(n) yields an approximation to the unit
       impulse.

I mean "approximate" in the sense that the maximum absolute error or
similar measure, should be minimized.  In particular, I am not
interested in a least-squares solution to (2).  Any help or pointers
to pertinent literature will be greatly appreciated.  Please email
replies to ashok@atrp.mit.edu; I'll summarize.

Ashok Chhabedia Popat    Swiss Federal Institute of Technology, Lausanne