Reg Edwards wrote:
. . .
I came across Gibbs around 1948 by accident while searching for more
information on transmission lines in general. Google had not been invented.
He appears to have made his name known (no doubt also in other matters)
because of his "Gibb's Phenomenon", an overshoot of some kind in an
extension of Fourier's Waveform Analysis. At the time I had no interest in
'overshoots' and forgot all about it. . .
. . .

It's commonly known that a square wave consists of a sine wave of the
square wave's fundamental frequency, plus all its odd harmonics.
Specifically, all components are in phase, and their amplitudes are the
inverse of the harmonic number. That is, if the amplitude of the
fundamenatal sine wave is 1, the amplitude of the third harmonic is 1/3,
the amplitude of the fifth harmonic is 1/5, and so forth.

So we should be able to create a square wave by adding all those sine
waves -- right?

It turns out that if we add the first few sine wave components, we have
a fairly square looking wave -- but it has an overshoot at the leading
and trailing edges. As we add more and more harmonics, the result gets
more square, and the overshoot gets narrower and narrower -- but it
remains, and with the same amplitude. Although the width approaches zero
as the number of sine waves you've added gets infinite, there's always
an overshoot for any finite number of sine waves.

This is one manifestation of the Gibbs' Phenomenon, which also applies
to other situtations. There's a really nifty demo at
http://klebanov.homeip.net/~pavel/fb...applets/Gibbs/.

Roy Lewallen, W7EL