Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on $\mathbbR$
<|reference_start|>Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on $\mathbbR$: 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.<|reference_end|>
@article{ehler2024quantitative,
    title={Quantitative estimates: How well does the discrete Fourier transform
  approximate the Fourier transform on $\mathbb{R}$},
    author={Martin Ehler and Karlheinz Gr"ochenig and Andreas Klotz},
    journal={arXiv preprint arXiv:2403.03810},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.03810},
    primaryClass={math.NA cs.NA}
}