Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on $\mathbb{R}$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909965688504320 |
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| author | Ehler, Martin Gröchenig, Karlheinz Klotz, Andreas |
| author_facet | Ehler, Martin Gröchenig, Karlheinz Klotz, Andreas |
| contents | In order to compute the Fourier transform of a function $f$ on the real line numerically, one samples $f$ on a grid and then takes the discrete Fourier transform. We derive exact error estimates for this procedure in terms of the decay and smoothness of $f$. The analysis provides a new recipe of how to relate the number of samples, the sampling interval, and the grid size. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_03810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on $\mathbb{R}$ Ehler, Martin Gröchenig, Karlheinz Klotz, Andreas Numerical Analysis 42QA38, 65T05, 94A12, 43A15 In order to compute the Fourier transform of a function $f$ on the real line numerically, one samples $f$ on a grid and then takes the discrete Fourier transform. We derive exact error estimates for this procedure in terms of the decay and smoothness of $f$. The analysis provides a new recipe of how to relate the number of samples, the sampling interval, and the grid size. |
| title | Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on $\mathbb{R}$ |
| topic | Numerical Analysis 42QA38, 65T05, 94A12, 43A15 |
| url | https://arxiv.org/abs/2403.03810 |