Uniform error estimates for nonequispaced fast Fourier transforms

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 the optimal choice from the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter.