"On numerical realizations of Shannon’s sampling theorem"Kircheis, MelanieAs known, classical Shannon sampling sums suffer from slow convergence and numerical instability in the presence of noise in the samples. Therefore, in this talk we discuss some numerical realizations of Shannon's sampling theorem. To overcome the aforementioned limitations, one can use oversampling and regularization with a suitable window function. Since such a window function can be chosen either in the frequency domain or in the spatial domain, we compare these two approaches, especially in terms of error decay rates. We show that the best numerical results are obtained by oversampling and regularization in the spatial domain, resulting in an interpolating approximation with localized sampling. Addionally, numerical experiments illustrate the theoretical results. |
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