Continuous window functions for NFFT

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/discontinuous Kaiser--Bessel, continuous $\exp$-type, and continuous $\cosh$-type window functions. We present novel explicit error estimates for NFFT with such a window function 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. For the considered window functions, the error constants have an exponential decay with respect to the truncation parameter.