The Poisson summation formula is a powerful and essential result in analytic number theory and Fourier analysis, connecting sums of a function at integer points to sums of its Fourier transform. Specifically, it relates a sum over a lattice (for example, the integers) to a sum over the dual lattice.
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For a sufficiently rapidly decreasing function , the Poisson summation formula relates its samples to those of its Fourier transform:under the convention .