A Method for Validating Multidimensional Fast Fourier Transform (FFT) Algorithms

TLDR: The general motivation for the work comes from the need to validate the FFT algorithm when it newly implemented on a computer or when new techniques or devices are added to a computer facility to evaluate discrete Fourier transforms.

Abstract: : A method is described for validating fast Fourier transforms (FFTs) based on the use of simple input functions whose discrete Fourier transforms can be evaluated in closed form Explicit analytical results are developed for one dimensional and two dimensional discrete Fourier transforms The analytical results are easily generalized to higher dimensions The results offer a means for validating the FFT algorithm in one, two, or higher dimensional settings The general motivation for the work comes from the need to validate the FFT algorithm when it newly implemented on a computer or when new techniques or devices are added to a computer facility to evaluate discrete Fourier transforms Keywords: Computer Program Verification