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Quantitative Estimates: How Well Does the Discrete Fourier Transform Approximate the Fourier Transform on R?
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DOI：10.1137/24M1650399.png)
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Abstract
En 中文
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 an asymptotically optimal recipe for how to relate the number of samples, the sampling interval, and the grid size.
Keywords:
discrete Fourier transform
FFT
approximation rate
weight function
amalgam space
Journal
IF:
6.1
Papers:
888
Citations:
1.2W
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Cited Papers