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From: slag@charm.UUCP (Peter Rosenthal)
Newsgroups: net.audio
Subject: Re: Square waves (and an oops)
Message-ID: <381@charm.UUCP>
Date: Fri, 22-Jun-84 15:10:44 EDT
Article-I.D.: charm.381
Posted: Fri Jun 22 15:10:44 1984
Date-Received: Wed, 27-Jun-84 01:33:39 EDT
References: <3821@mordor.UUCP> <28@sunybcs.UUCP>, <558@opus.UUCP>
Organization: Physics Research - AT&T Bell Labs MH
Lines: 18

I can hear x-rays.



	There is a little known phenomenon pertinent to this discussion.
It is known as the gibbs phenomenon.  Basically, it amounts to the
following:

	Given a square wave approximated by additive synthesis, it
is generally true that there will be an overshoot of eight percent
at the step.  This remains true as more and more components are
included.  As the approximation gets better and better, the
overshoot does not improve, it only gets narrower.  In the
limiting case it becomes infinitely narrow.

	Josiah Willard Gibbs, the father of statistical mechanics
is responsible for this gem, but I don't know the details
of the work.