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Prolog to Sampling—50 Years After Shannon

R. 0’Donnell

Proceedings of the IEEE, vol. 88, no. 4, pp. 567-568, April 2000.



It has been 50 years since Claude Shannon laid the foundation for information theory with the publication of “Communication in the Presence of Noise.” In that paper, Shannon articulated the theorem that information could be quantified and coded by a mathematical process of sampling. The intervening years have proved Shannon's paper to be a major theoretical work, one that has had the greatest impact on modern electrical engineering. In this tutorial, the author revisits Shannon's original sampling paradigm to see how well it stands up to modern requirements and how it may be extended to accommodate today's larger selection of sampling functions. This includes an examination of standard sampling methodology as it relates to current technology, the application of Shannon's theorem to wavelet theory, methods for controlling approximation error, and variations and extensions of sampling theory.


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