Continuous window functions for NFFT

TL;DR

This paper analyzes the error behavior of the NFFT algorithm using various continuous window functions, providing explicit error estimates and guidelines for optimal parameter selection to improve accuracy.

Contribution

It introduces novel explicit error estimates for NFFT with continuous window functions and derives rules for optimal parameter choices, enhancing the understanding of error decay.

Findings

Error constants decay exponentially with the truncation parameter.

Explicit error estimates are provided for multiple continuous window functions.

Guidelines for optimal parameter selection in NFFT are established.

Abstract

In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. Here we consider the continuous Kaiser--Bessel, continuous $\exp$-type, $\sinh$-type, and continuous $\cosh$-type window functions with the same support and same shape parameter. We present novel explicit error estimates for NFFT with such a window function and derive rules for the optimal choice of the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter. For the considered continuous window functions, the error constants have an exponential decay with respect to the truncation parameter.