Nonequispaced fast Fourier transforms for bandlimited functions

Melanie Kircheis, Daniel Potts

Session: General

Keywords: nonequispaced fast Fourier transform, bandlimited functions, regularized Shannon sampling formulas, sinc function, NFFT, NUFFT

TL;DR: We introduce a new NFFT-like procedure for bandlimited functions, which is based on regularized Shannon sampling formulas.

Abstract:

In this paper we consider the problem of approximating function evaluations $f(\boldsymbol x_j)$ at given nonequispaced points $\boldsymbol x_j$, $j=1,\dots N,$ of a bandlimited function from given values $\hat{f}(\boldsymbol k)$, $\boldsymbol k\in \mathcal I_{\boldsymbol M}$, 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.

Submission Number: 112