2020/10/31 by Daniel Potts, Manfred Tasche
Computer Science · Mathematics · Medicine · #Algorithm #Applied mathematics #Bessel function #Computer science #Constant (computer programming) #Continuous function (set theory) #Error function #Exponential function #Fourier transform #Function (biology) #Geometry #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Statistics #Trigonometric functions #Truncation (statistics) #Truncation error #Ultrasound Imaging and Elastography #Window (computing) #Window function #cs.NA #math.NA #msc:42A10 #msc:65T50 #msc:94A12
paper · pdf · doi:10.1007/s10444-021-09873-8
published as Advances in Computational Mathematics volume 47, Article number: 53 (2021)
arxiv created 2021/02/11 · openalex publication_date 2021/06/30 · arxiv updated 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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. Here, we consider the continuous Kaiser–Bessel, continuous exp-type, sinh-type, and continuous cosh-type window functions with the same support and same shape parameter. We present novel explicit error estimates for NFFT with such a window function and derive rules for the optimal choice of 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 continuous window functions, the error constants have an exponential decay with respect to the truncation parameter.