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Journal of Applied Mathematics
Volume 2012, Article ID 102039, 9 pages
Research Article

The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform

Department of Basic Science, Beijing University of Agriculture, Beijing 102206, China

Received 1 August 2012; Revised 24 November 2012; Accepted 24 November 2012

Academic Editor: Baolin Wang

Copyright © 2012 Jun-Fang Zhang and Shou-Ping Hou. 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.


The generalization of the classical Poisson sum formula, by replacing the ordinary Fourier transform by the canonical transformation, has been derived in the linear canonical transform sense. Firstly, a new sum formula of Chirp-periodic property has been introduced, and then the relationship between this new sum and the original signal is derived. Secondly, the generalization of the classical Poisson sum formula to the linear canonical transform sense has been obtained.