Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GIBBS PHENOMENON AND CERTAIN NONHARMONIC FOURIER SERIES

  • Rhee, Jung-Soo (DEPARTMENT OF MATHEMATICS PUSAN UNIVERSITY OF FOREIGN STUDIES)
  • Received : 2010.01.15
  • Published : 2011.01.31
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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.

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References

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