Two-dimensional Gibbs Phenomenon for Fractional Fourier Series and its Resolution

摘要：

The truncated Fourier series exhibits oscillation that does not disappear as the number of terms in the truncation is increased. This paper introduces 2-D fractional Fourier series (FrFS) according to the 1-D fractional Fourier series, and finds such a Gibbs oscillation also occurs in the partial sums of FrFS for bivariate functions at a jump discontinuity. In this study, the 2-D inverse polynomial reconstruction method (IPRM) which is a method based on the inversion of the transformation matrix that represents the fraction Fourier space has been used to remove the Gibbs effect. The aim of this study is to verify the 2-D IPRM has the similar effection for removing the Gibbs oscillation for partial fractional Fourier sums of bivariate functions. Numerical experiments verify the efficiency and accuracy of IPRM.

关键词： fractional Fourier series Gibbs phenomenon inverse polynomial reconstruction method Gegenbauer polynomials

作者: Meiyu Ding Hongqing Zhu Zongfeng Nie

作者单位: Department of Electronics and Communications Engineering,East China University of Science and Technology Shanghai 200237, China

会议类型: 国际会议

会议名称: 2011 International Conference on Communication and Electronics Information(ICCEI 2011)(2011年通信和电子信息国际会议)

会议地点: 海口

会议语种:英文

页码: 122-126

在线出版日期: 2011-02-22（万方平台首次上网日期，不代表论文的发表时间）