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.
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Acknowledgements
The authors would like to thank Stefan Kunis and Elias Wegert for several fruitful discussions on the topic. The authors are grateful to the anonymous referees for helpful comments and suggestions.
Funding
Open Access funding enabled and organized by Projekt DEAL. The first author received funding from the Deutsche Forschungsgemeinschaft (German Research Foundation) – Project–ID 416228727 – SFB 1410.
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Communicated by: Anna-Karin Tornberg
Dedicated to Jürgen Prestin on the occasion of his 60th birthday
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Potts, D., Tasche, M. Continuous window functions for NFFT. Adv Comput Math 47, 53 (2021). https://doi.org/10.1007/s10444-021-09873-8
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DOI: https://doi.org/10.1007/s10444-021-09873-8
Keywords
- Nonequispaced fast Fourier transform
- NFFT
- Error estimate
- Oversampling factor
- Truncation parameter
- Continuous window function with compact support
- Kaiser–Bessel window function