Quantitative estimates: How well does the discrete Fourier transform approximate the Fourier transform on ℝ
arxiv(2024)
摘要
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.
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