Eigenfunctions of the 2D finite Fourier transform 1

Abstract

A new powerful approach to compute the eigenfunctions of the finite two-dimensional Fourier transform is developed and analysed. The numerical technique is a generalization of an earlier method developed for ordinary prolate spheroidal wave functions. Special considerations are given to the problem of singularities and the procedure to locate the eigenvalues. It is demonstrated that the computations are fundamentally improved by the introduction of appropriate auxiliary differential equations.