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Journal of Applied Mathematics
Volume 2012, Article ID 428142, 11 pages
Research Article

Parseval Relationship of Samples in the Fractional Fourier Transform Domain

School of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 8 February 2012; Revised 13 April 2012; Accepted 8 May 2012

Academic Editor: Huijun Gao

Copyright © 2012 Bing-Zhao Li and Tian-Zhou Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.