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. Consequently, the periodic summation of a function is completely defined by discrete samples of the original function's Fourier transform. And conversely, the periodic summation of a function's Fourier transform is completely defined by discrete samples of the original function. The Poisson summation formula was discovered by
Siméon Denis Poisson and is sometimes called
Poisson resummation.