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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
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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