Newsgroups: comp.dsp Path: utzoo!utgpu!cunews!wilf From: wilf@sce.carleton.ca (Wilf Leblanc) Subject: Re: Complementary filters Message-ID: Sender: news@ccs.carleton.ca (news) Organization: Carleton University, Ottawa, Canada References: <9441@pasteur.Berkeley.EDU> <77352@sgi.sgi.com> Date: 7 Dec 90 21:04:05 GMT karsh@trifolium.esd.sgi.com (Bruce Karsh) writes: >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. >Generate one of the too signals, e.g. the low passed signal. Subtract it >from the original signal to get the high passed signal. > Bruce Karsh > karsh@sgi.com This is a nice idea, but it won't work in general. If H(z) is the low pass prototype, then, 1 - H(z) is a high pass ? No, sorry this does not work. i.e., say H(e^jw) = j (at a certain low frequency). Then 1 - H(e^jw) = 1 - j (which is nothing like a high pass). 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 ?? -- Wilf LeBlanc Carleton University Internet: wilf@sce.carleton.ca Systems & Computer Eng. UUCP: ...!uunet!mitel!cunews!sce!wilf Ottawa, Ont, Canada, K1S 5B6