The Poisson Summation Formula is an identity relating the periodic summation of a function to the values of that function's continuous Fourier transform, so that the Fourier series coefficients of the periodized function are exactly given by discrete samples of the transform, and conversely. Discovered by Simeon Denis Poisson, it is a fundamental tool of Fourier analysis that links a function's behavior in physical space to its behavior in frequency space, with applications ranging from number theory to signal processing.
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StatementThe Poisson summation formula relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. 1 Classification
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1. Poisson summation formula (Wikipedia)
Lead paragraph
In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform.
In Branch: Harmonic Analysis, Lead section
Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation
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