Nonequispaced fast Fourier transforms for bandlimited functions

Abstract

In this paper we consider the problem of approximating function evaluations $f({\mathbf{x}}_j)$ at given nonequispaced points ${\mathbf{x}}_j$, $j=1,\dots N$, of a bandlimited function from given values $\hat{f}(\mathbf{k})$, $\mathbf{k}\in {\mathcal{I}}_{\mathbf{M}}$, of its Fourier transform. Note that if a trigonometric polynomial is given, it is already known that this problem can be solved by means of the nonequispaced fast Fourier transform (NFFT). In other words, we introduce a new NFFT-like procedure for bandlimited functions, which is based on regularized Shannon sampling formulas.