Gibbs phenomenon removal by adding Heaviside functions

Authors:
Kyung Soo Rim;Beong In Yun
Affiliations:
Department of Mathematics, Sogang University, Seoul, Korea 121-742;Department of Infor. & Stat., Kunsan National University, Kunsan, Korea 573-701
Venue:
Advances in Computational Mathematics
Year:
2013

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Abstract

We define a kind of spectral series to filter off completely the Gibbs phenomenon without overshooting and distortional approximation near a point of discontinuity. The construction of this series is based on the method of adding the Fourier coefficients of a Heaviside function to the given Fourier partial sums. More precisely, we prove the uniform convergence of the proposed series on the class of piecewise smooth functions. Also, we attach two numerical examples which illustrate the uniform convergence of the suggested series in comparison with the Fourier partial sums.