A new technique for calculating fourier integrals based on the poisson summation formula

This paper derives a general method for the calculation of Fourier integrals based on the Poisson summation formula. The approach is an extension of that due to Medhurst (1960) and can be thought of as an extension of the Mobius inversion formula. Useful applications are to the calculation of probability density funtions from their Fourier transforms.