Gibbs phenomenon

The Gibbs phenomenon, first observed by Albert Michelson via a mechanical graphing machine and first explained by Willard Gibbs, is the peculiar mode in which the Fourier series of a piecewise continuous periodic function f fails to converge uniformly to f.

At a jump discontinuity of f, the nth partial sum of the Fourier series jumps too far and overshoots its target.

External links

• Why are sine waves fundamental
• Gibbs phenomenon - from mathworld
• " class="external">http://lcavwww.epfl.ch/~prandoni/dsp/gibbs/gibbs.html

This is a very stubby article. What appears above needs to be made precise and explicit. At least one graphical illustration should be added.