Gibbs' phenomenon

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Gibbs' phenomenon

[′gibz fə‚näm·ə‚nän]
(mathematics)
A convergence phenomenon occurring when a function with a discontinuity is approximated by a finite number of terms from a Fourier series.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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This deficiency of the spectral approximation results in the so-called Gibbs phenomenon which shows nonvanishing spikes near the discontinuity [1,2].
In this work, focusing on the Fourier partial sum approximation for a piecewise smooth function f having a jump-discontinuity [xi], we aim to develop a constructive approximation procedure which is available for eliminating the Gibbs phenomenon near the discontinuity.
Gibbs Phenomenon. The complex amplitude of a wavefront obtained by a uniformly collimated monochromatic beam of light reflected from an object is given by
Summability techniques were also applied on some engineering problems; for example, Chen and Jeng [9] implemented the Cesaro sum of order (C, 1) and (C, 2), in order to accelerate the convergence rate to deal with the Gibbs phenomenon, for the dynamic response of a finite elastic body subjected to boundary traction.
But Gibbs phenomenon occurs when the Fourier representation method is applied to a non-periodic or discontinuous function [6].
Using Mathematica students were able to visualise Fourier series of functions and explore Gibbs phenomenon which is usually a part of college mathematics.
This effect is called the Gibbs phenomenon and caused by the very slow convergence of a truncated Fourier series near a discontinuity.
Over the years Abdul's wide-ranging research interests have been in integral and discrete transforms where he was an innovator of iterative methods for nonlinear problems, sampling expansions, the Gibbs phenomenon and operational sum methods for difference equations.
One mathematical effect, the Gibbs phenomenon, can add anomalies to a signal.
Jerri, The Gibbs Phenomenon in Fourier Analysis, Splines, and Wavelet Application.
In this case, the well-known Gibbs phenomenon reduces the order of accuracy to first order and produces spurious oscillations, particularly ill regions near the discontinuities.