Gibbs phenomenon and certain nonharmonic Fourier series
Commun. Korean Math. Soc. 2011 Vol. 26, No. 1, 89-98
https://doi.org/10.4134/CKMS.2011.26.1.89
Published online March 1, 2011
Jungsoo Rhee
Pusan University of Foreign Studies
Abstract : The Fourier series has a rapid oscillation near end points at jump discontinuity which is called the Gibbs phenomenon. There is an overshoot (or undershoot) of approximately 9\% at jump discontinuity. In this paper, we prove that a bunch of series representations (certain nonharmonic Fourier series) give good approximations vanishing Gibbs phenomenon. Also we have an application for approximating some shape of upper part of a vehicle in a different way from the method of cubic splines and wavelets.
Keywords : Gibbs phenomenon, certain nonharmonic Fourier series, splines and wavelets
MSC numbers : 42A20, 42A24
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