Computation of Fourier Transforms for Noisy Bandlimited Signals

Authors:
Weidong Chen
Affiliations:
chenw@math.ksu.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

Citing 4
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An Efficient Method for an Ill-Posed Problem — Band-Limited Extrapolation by Regularization

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Abstract

In this paper, the ill-posed problem of computation of the Fourier transform $\hat{f}$ for a noisy bandlimited signal $f$ is discussed. Here, $\hat{f}$ is computed by a regularized Fourier series which is obtained by a regularization of the Fourier transformed sampling formula of Shannon. If the regularization parameter tends to zero, the uniform and $L^2$-convergence of this method is proved. Numerical examples show the performance of this approach.