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Shannon sampling and function reconstruction from point values. (English) Zbl 1107.94007
This important paper constructs a new framework for understanding Shannon’s sampling theorem and throws light on the relations among sampling theory, learning theory and statistics. It proposes a measure of the richness of the data, which is used to substitute the bandwidth in standard sampling theorem, so that the error of reconstructing a signal from observed noised data is analyzed in a novel method.

MSC:
94A20 Sampling theory in information and communication theory
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
68T05 Learning and adaptive systems in artificial intelligence
68U10 Computing methodologies for image processing
41A05 Interpolation in approximation theory
62J05 Linear regression; mixed models
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