Two-Dimensional gibbs phenomenon for fractional fourier series and its resolution

Authors:
Meiyu Ding;Hongqing Zhu
Affiliations:
Department of Electronics and Communications Engineering, East China University of Science and Technology, Shanghai, China;Department of Electronics and Communications Engineering, East China University of Science and Technology, Shanghai, China
Venue:
AICI'12 Proceedings of the 4th international conference on Artificial Intelligence and Computational Intelligence
Year:
2012

Citing 6
Cited 0

On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function

Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
On the Gibbs Phenomenon and Its Resolution

SIAM Review
Towards the resolution of the Gibbs phenomena

Journal of Computational and Applied Mathematics
Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon

Journal of Computational and Applied Mathematics
Inverse Polynomial Reconstruction of Two Dimensional Fourier Images

Journal of Scientific Computing
Fractional Fourier series expansion for finite signals and dualextension to discrete-time fractional Fourier transform

IEEE Transactions on Signal Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.