Two-dimensional fractional Fourier transform and some of its properties

2018 ◽  
Vol 29 (7) ◽  
pp. 553-570 ◽  
Author(s):  
Ahmed Zayed
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Two Dimensional

scholarly journals The Solvability of a Class of Convolution Equations Associated with 2D FRFT

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1928
Author(s):  
Zhen-Wei Li ◽  
Wen-Biao Gao ◽  
Bing-Zhao Li
Keyword(s):  
Fourier Transform ◽  
Convolution Operator ◽  
Fractional Fourier Transform ◽  
Hankel Transform ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Spatial Shift ◽  
Fractional Hankel Transform ◽  
The Relationship ◽  
Convolution Equations

In this paper, the solvability of a class of convolution equations is discussed by using two-dimensional (2D) fractional Fourier transform (FRFT) in polar coordinates. Firstly, we generalize the 2D FRFT to the polar coordinates setting. The relationship between 2D FRFT and fractional Hankel transform (FRHT) is derived. Secondly, the spatial shift and multiplication theorems for 2D FRFT are proposed by using this relationship. Thirdly, in order to analyze the solvability of the convolution equations, a novel convolution operator for 2D FRFT is proposed, and the corresponding convolution theorem is investigated. Finally, based on the proposed theorems, the solvability of the convolution equations is studied.

The Laguerre-Gaussian series representation of two-dimensional fractional Fourier transform

1998 ◽  
Vol 31 (46) ◽  
pp. 9353-9357 ◽  
Author(s):  
Li Yu ◽  
Wenda Huang ◽  
Meichun Huang ◽  
Zizhong Zhu ◽  
Xiaoming Zeng ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Series Representation ◽  
Two Dimensional ◽  
Gaussian Series

scholarly journals Parseval Relationship of Samples in the Fractional Fourier Transform Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Bing-Zhao Li ◽  
Tian-Zhou Xu
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Dimensional Case ◽  
Fourier Domain ◽  
Transform Domain ◽  
Two Dimensional ◽  
Band Limited ◽  
Relationship Of ◽  
The Relationship ◽  
Fourier Transform Domain

This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained. Then, the relationship is extended to a general set of nonuniform samples of band-limited signal associated with the fractional Fourier transform. Finally, the two dimensional case is investigated in detail, it is also shown that the derived results can be regarded as the generalization of the classical ones in the Fourier domain to the fractional Fourier transform domain.

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