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From: karsh@trifolium.esd.sgi.com (Bruce Karsh)
Newsgroups: comp.dsp
Subject: Re: 180 deg phase shift
Message-ID: <103038@sgi.sgi.com>
Date: 10 May 91 12:55:30 GMT
References: <1991May9.160115.3494@cpsc.ucalgary.ca> <1991May09.192740.4165@bmerh2.bnr.ca>
Sender: news@sgi.sgi.com
Reply-To: karsh@trifolium.sgi.com (Bruce Karsh)
Organization: Silicon Graphics, Inc., Mountain View, CA
Lines: 13

>>Given *ANY* signal  x(n)  with Fourier Transform  X(w)
>Really? You surely mean _periodic_ signal.

A signal doesn't have to be periodic to have a Fourier transform.  Any
sequence x(n) that is absolutely summable (i.e., the sum of the absolute
values is bounded) has a Fourier transform given by:

	       inf	
	X(w) = sum	  x(n)e^(-jwn)
	       n = -inf

			Bruce Karsh
			karsh@sgi.com