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.

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.

Chaotic encryption of images in the fractional Fourier transform domain using different modes of operation

2013 ◽  
Vol 9 (3) ◽  
pp. 611-622 ◽  
Author(s):  
Heba M. Elhoseny ◽  
Hossam E. H. Ahmed ◽  
Alaa M. Abbas ◽  
Hassan B. Kazemian ◽  
Osama S. Faragallah ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Transform Domain ◽  
Chaotic Encryption ◽  
Modes Of Operation ◽  
Fourier Transform Domain

Beam shaping in the fractional Fourier transform domain

1998 ◽  
Vol 15 (5) ◽  
pp. 1114 ◽  
Author(s):  
Yan Zhang ◽  
Bi-Zhen Dong ◽  
Ben-Yuan Gu ◽  
Guo-Zhen Yang
Keyword(s):  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Beam Shaping ◽  
Transform Domain ◽  
Fourier Transform Domain
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