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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

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