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.
Highlights
Since the restriction to equispaced data is an essential drawback in several applications of discrete Fourier transform, one has developed fast algorithms for nonequispaced data, the so-called nonequispaced fast Fourier transform (NFFT), see [6,8,11,12,20, 24] and [18, Chapter 7].Communicated by Gerlind Plonka. 17 Page 2 of 42D
In this paper we investigate error estimates for the NFFT, where we restrict ourselves to an approximation by translates of a previously selected, continuous window function with compact support
We show that the Bessel window function (39), sinh-type window function (45), and modified cosh-type window function (46) are very convenient for NFFT, since they possess very small C(T)-error constants with exponential decay with respect to m
Summary
Since the restriction to equispaced data is an essential drawback in several applications of discrete Fourier transform, one has developed fast algorithms for nonequispaced data, the so-called nonequispaced fast Fourier transform (NFFT), see [6,8,11,12,20, 24] and [18, Chapter 7].
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