Automated parameter tuning based on RMS errors for nonequispaced FFTs

In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the ℒ 2 -norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shap...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 42; no. 4; pp. 889 - 919
Main Author Nestler, Franziska
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2016
Subjects
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Visualization
NFFT
Nonuniform fast Fourier transform
Nonequispaced fast Fourier transform
65T
NUFFT
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Summary:In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the ℒ 2 -norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-015-9446-8