Uniform error estimates for nonequispaced fast Fourier transforms

TL;DR

This paper provides new error estimates for the nonequispaced fast Fourier transform (NFFT) using compactly supported window functions, offering guidelines for parameter choices to optimize accuracy.

Contribution

It introduces novel error bounds for NFFT with continuous window functions and derives practical rules for selecting parameters based on the error constants.

Findings

Error constants depend mainly on oversampling factor and truncation parameter.

New error estimates improve understanding of NFFT accuracy.

Guidelines for choosing window functions and parameters are provided.

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. So far, various window functions have been used and new window functions have recently been proposed. We present novel error estimates for NFFT with compactly supported, continuous window functions and derive rules for convenient choice from the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter.