Affiliation:
1. School of Mathematics Science, Jiangsu University, Zhenjiang 212013, P. R. China
2. School of Mathematical Science, Yangzhou University, Yangzhou 225002, P. R. China
Abstract
The fractional Fourier transform (FRFT) is a generalized form of the Fourier transform (FT), it is another important class of time–frequency analysis tool in signal processing. In this paper, we study the two-dimensional (2D) FRFT in the polar coordinates setting. First, Parseval theorem of the 2D FRFT in the polar coordinates is obtained. Then, according to the relationship between 2D FRFT and fractional Hankel transform (FRHT), the convolution theorem for the 2D FRFT in polar coordinates is obtained. It shows that the FRFT of the convolution of two functions is the product of their respective FRFTs. Moreover, the fast algorithm for the convolution theorem of the 2D FRFT is discussed. Finally, the sampling theorem for signal is explored.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Higher Education Institutions of China
Lv Yang Jin Feng Plan of Yangzhou city
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Information Systems,Signal Processing