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From: varri@news.funet.fi.tut.fi (V{rri Alpo)
Newsgroups: comp.dsp
Subject: Re: Complementary filters
Message-ID: <1990Dec8.094311.11191@funet.fi>
Date: 8 Dec 90 09:43:11 GMT
References: <wilf.660603845@rigel.sce.carleton.ca>
Sender: news@funet.fi (#News )
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>>>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? 
> 
>>Generate one of the too signals, e.g. the low passed signal.  Subtract it
>>from the original signal to get the high passed signal.
> 
> This is a nice idea, but it won't work in general.
> i.e. simple subtraction doesn't consider the phase response of H(z).
> Something must have been written on this, what about Quadrature Mirror
> Filterbanks ??

You could try this one: Tree-Structured Complementary Filter Banks
Using All-Pass Sections, Regalia P, Mitra S, Vaidyanathan P, Renfors
M, Neuvo Y. IEEE Transactions on Circuits and Systems, Vol. CAS-34,
No. 12, Dec. 1987.