The Resolution of the Gibbs Phenomenon for Fractional Fourier Series

摘要：

The nth partial sums of a classical Fourier series have large oscillations near the jump discontinuities. This behavior is the well-known Gibbs phenomenon. Recently, the inverse polynomial reconstruction method (IPRM) has been successfully implemented to reconstruct piecewise smooth functions by reducing the effects of the Gibbs phenomenon for Fourier series. This paper addresses that the similar phenomenon will be observed in fractional Fourier series (FrFS) expansion, and expects that the existed IPRM for resolution of the Gibbs phenomenon for FrFS appears to be the same as for Fourier series. Two numerical examples are investigated. The result indicates that the IPRM method completely eliminates Gibbs phenomenon and gives exact reconstruction results.

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

作者: Hongqing Zhu Meiyu Ding

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: 1-5

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）