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.
Jun-Fang Zhang. Shou-Ping Hou. "The Generalization of the Poisson Sum Formula Associated with the Linear Canonical Transform." J. Appl. Math. 2012 1 - 9, 2012. https://doi.org/10.1155/2012/102039