Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on $\mathbb{R}$
Numerical Analysis
2025-12-18 v2 Numerical Analysis
Abstract
In order to compute the Fourier transform of a function on the real line numerically, one samples 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 . The analysis provides a new recipe of how to relate the number of samples, the sampling interval, and the grid size.
Cite
@article{arxiv.2403.03810,
title = {Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on $\mathbb{R}$},
author = {Martin Ehler and Karlheinz Gröchenig and Andreas Klotz},
journal= {arXiv preprint arXiv:2403.03810},
year = {2025}
}
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27 pages