Nonuniform fast Fourier transforms with nonequispaced spatial and frequency data and fast sinc transforms
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866908395489984512 |
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| author | Kircheis, Melanie Potts, Daniel Tasche, Manfred |
| author_facet | Kircheis, Melanie Potts, Daniel Tasche, Manfred |
| contents | In this paper we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as its application. The computation of NNFFT is mainly based on the nonuniform fast Fourier transform with nonequispaced spatial nodes and equispaced frequencies (NFFT). The NNFFT employs two compactly supported, continuous window functions. For fixed nonharmonic bandwidth, it is shown that the error of the NNFFT with two sinh-type window functions has an exponential decay with respect to the truncation parameters of the used window functions. As an important application of the NNFFT, we present the fast sinc transform. The error of the fast sinc transform is estimated as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_02671 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nonuniform fast Fourier transforms with nonequispaced spatial and frequency data and fast sinc transforms Kircheis, Melanie Potts, Daniel Tasche, Manfred Numerical Analysis 65T50, 94A12, 94A20 In this paper we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) and the fast sinc transform as its application. The computation of NNFFT is mainly based on the nonuniform fast Fourier transform with nonequispaced spatial nodes and equispaced frequencies (NFFT). The NNFFT employs two compactly supported, continuous window functions. For fixed nonharmonic bandwidth, it is shown that the error of the NNFFT with two sinh-type window functions has an exponential decay with respect to the truncation parameters of the used window functions. As an important application of the NNFFT, we present the fast sinc transform. The error of the fast sinc transform is estimated as well. |
| title | Nonuniform fast Fourier transforms with nonequispaced spatial and frequency data and fast sinc transforms |
| topic | Numerical Analysis 65T50, 94A12, 94A20 |
| url | https://arxiv.org/abs/2107.02671 |