Abstract
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.
Highlights
IntroductionThe 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
The objective of this paper is to study and investigate the Poisson formula associated with the LCT
Suppose a signal x t is band-limited to ΩA in linear canonical transform domain of parameter A, from 2.10 a new function y t can be deduced from signal x t
Summary
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. The generalization of the classical Poisson sum formula to the linear canonical transform sense has been obtained. The Poisson summation formula is a very useful tool in many branches of the mathematics, and it finds many applications in various fields, for example, mechanics, signal processing community, and many scientific fields.
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