Article View: comp.dsp
Article #1357Re: Complementary filters
From: Joe Buck
Date: Wed, 05 Dec 1990 19:24
Date: Wed, 05 Dec 1990 19:24
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1280 bytes
In article <9441@pasteur.Berkeley.EDU>, maverick@fir.Berkeley.EDU (Vance Maverick) writes:
> Is there a recipe for generating the "complement" of a given filter? Or
> for generating a pair of filters which are complementary in this sense?
> I've seen the basic transformations between lowpass and highpass
> filters, and I don't think they qualify.
It's easy. You want the two filters to sum to one; equivalently, you
want the sums of the two impulse responses to sum to 1 for n=0 and
0 for everywhere else. Let's say you have an FIR filter and you want
its complement. Let h(n) be the value of the nth tap of the filter.
Then
c(0) = 1 - h(0)
c(n) = -h(n), n > 0
Voila. Note that the outputs of the two filters sum to give the
original signal back.
--
Joe Buck
jbuck@galileo.berkeley.edu {uunet,ucbvax}!galileo.berkeley.edu!jbuck
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Path: arc1-ca.pugleaf.net!utzoo!attcan!uunet!peregrine!elroy.jpl.nasa.gov!usc!apple!agate!ucbvax!galileo.berkeley.edu!jbuck From: jbuck@galileo.berkeley.edu (Joe Buck) Newsgroups: comp.dsp Subject: Re: Complementary filters Message-ID: <39905@ucbvax.BERKELEY.EDU> Date: 5 Dec 90 19:24:19 GMT References: <9441@pasteur.Berkeley.EDU> Sender: usenet@ucbvax.BERKELEY.EDU Reply-To: jbuck@galileo.berkeley.edu (Joe Buck) Lines: 21