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GIBBS PHENOMENON AND CERTAIN NONHARMONIC FOURIER SERIES

  • Received : 2010.01.15
  • Published : 2011.01.31

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

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