# 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.
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But Gibbs phenomenon occurs when the Fourier representation method is applied to a non-periodic or discontinuous function .
The Inverse Polynomial Reconstruction Method (IPRM) presents a basis-independent reconstruction frame to overcome the Gibbs phenomenon [12,15,17].
Using Mathematica students were able to visualise Fourier series of functions and explore Gibbs phenomenon which is usually a part of college mathematics.
The study is based on a laboratory module on exploring Fourier series and Gibbs phenomenon which was undertaken with 32 year 12 students (as a part of a project to investigate the effect of integrating computer algebra with traditional teaching.
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.
Abdul's fourth book is on a fascinating (but more specialized) research topic: The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations, [B 4].
One mathematical effect, the Gibbs phenomenon, can add anomalies to a signal.
For information about the Gibbs phenomenon, see--www.
Jerri, The Gibbs Phenomenon in Fourier Analysis, Splines, and Wavelet Application.
Jerri, Advances in the Gibbs Phenomenon, Sampling Publishing, Potsdam, New York, 2008, \$94.
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.

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