Fractional Fourier transform associated with polar coordinates

被引：0
作者：
Sun, Yan-Nan [1 ]
Gao, Wen-Biao [2 ]
机构：
[1] Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Peoples R China
[2] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Peoples R China
来源：
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING | 2024年 / 22卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Fractional Fourier transform; fractional Hankel transform; polar coordinates; convolution theorem; sampling theorem; RECONSTRUCTION; SIGNALS; THEOREMS; DOMAIN;
D O I：
10.1142/S0219691323500492
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
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.
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页数：12
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