Continuous window functions for NFFT

10/14/2020

∙

by   Daniel Potts, et al.

∙

0

∙

share

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 -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.