文献类型：期刊文献

英文题名：Two-dimensional Gibbs phenomenon for fractional fourier series and its resolution

作者：Ding, Meiyu[1]; Zhu, Hongqing[1]

机构：[1] Department of Electronics and Communications Engineering, East China University of Science and Technology, Shanghai 200237, China

年份：2012

卷号：7530 LNAI

起止页码：530

外文期刊名：Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

收录：EI(收录号：20124515642339)

语种：英文

外文关键词：Linear transformations - Polynomials - Fourier series

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 purpose 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. ? 2012 Springer-Verlag.