文献类型：期刊文献

英文题名：Gibbs phenomenon for fractional Fourier series

作者：Zhu, H.[1];Ding, M.[1];Li, Y.[1]

机构：[1]E China Univ Sci & Technol, Dept Elect & Commun Engn, Shanghai 200237, Peoples R China

年份：2011

卷号：5

期号：8

起止页码：728

外文期刊名：IET SIGNAL PROCESSING

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000298861700003)】；

基金：The authors would like to thank the anonymous referees for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China under grant no. 60975004.

语种：英文

摘要：It is well known that the partial sums of a Fourier series of a non-periodic analytic function on a finite interval exhibit spurious oscillations near the interval boundaries. This phenomenon is known as the Gibbs effect. The authors show that a similar phenomenon is observed for the fractional Fourier series (FrFS) of a function with jump discontinuities. The convergence of FrFS is discussed and proved in a theorem. Specifically, the present work proves the uniform convergence of the FrFS for a non-periodic analytic function in the smooth region. The maximum amplitude of the oscillations for the FrFS remains constant (the Gibbs constant), similar to that for a classical Fourier series expansion. Finally, three numerical examples are investigated to demonstrate that the Gibbs constant for an FrFS is the same as for a Fourier series.