Dictionary:Gibbs’ phenomenon

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When a waveform that includes a discontinuity (or whose derivatives are discontinuous) is Fourier synthesized, the fit is poor near the discontinuity. As the number of frequency components included in the synthesis increases, the region of poor fit becomes narrower, but some overshoot at discontinuities continues. The poor fit sometimes is called Gibbs’ ears. Named for Josiah Willard Gibbs (1839–1903), American mathematician and physicist. See Figure F-18 and Sheriff and Geldart (1995, 539–540).