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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.

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