Sinc integrals revisited

Abstract

The purpose of this paper is the evaluation of the Fourier transform of powers of the sinc function multiplied by monomials, also in the cases when log terms arise. Such evaluations appear only rarely in the literature. Some old sources are hardly available. Because of notations not in use today, several original works are difficult to read. We apply an approach by J. H. Michell in a variant of G. H. Hardy to integrals over sinc powers and their Fourier transforms. Moreover, the connection of such integrals with B‑splines is accentuated.