On the Duality of Discrete and Periodic Functions
AbstractAlthough versions of Poisson’s Summation Formula (PSF) have already been studied extensively, there seems to be no theorem that relates discretization to periodization and periodization to discretization in a simple manner. In this study, we show that two complementary formulas, both closely related to the classical Poisson Summation Formula, are needed to form a reciprocal Discretization-Periodization Theorem on generalized functions. We define discretization and periodization on generalized functions and show that the Fourier transform of periodic functions are discrete functions and, vice versa, the Fourier transform of discrete functions are periodic functions. View Full-Text
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Fischer, J.V. On the Duality of Discrete and Periodic Functions. Mathematics 2015, 3, 299-318.
Fischer JV. On the Duality of Discrete and Periodic Functions. Mathematics. 2015; 3(2):299-318.Chicago/Turabian Style
Fischer, Jens V. 2015. "On the Duality of Discrete and Periodic Functions." Mathematics 3, no. 2: 299-318.