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Authors = Gerhard Schmeisser

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35 pages, 396 KiB  
Article
Shannon’s Sampling Theorem for Bandlimited Signals and Their Hilbert Transform, Boas-Type Formulae for Higher Order Derivatives—The Aliasing Error Involved by Their Extensions from Bandlimited to Non-Bandlimited Signals
by Paul L. Butzer, Gerhard Schmeisser and Rudolf L. Stens
Entropy 2012, 14(11), 2192-2226; https://doi.org/10.3390/e14112192 - 5 Nov 2012
Cited by 30 | Viewed by 9346
Abstract
The paper is concerned with Shannon sampling reconstruction formulae of derivatives of bandlimited signals as well as of derivatives of their Hilbert transform, and their application to Boas-type formulae for higher order derivatives. The essential aim is to extend these results to non-bandlimited [...] Read more.
The paper is concerned with Shannon sampling reconstruction formulae of derivatives of bandlimited signals as well as of derivatives of their Hilbert transform, and their application to Boas-type formulae for higher order derivatives. The essential aim is to extend these results to non-bandlimited signals. Basic is the fact that by these extensions aliasing error terms must now be added to the bandlimited reconstruction formulae. These errors will be estimated in terms of the distance functional just introduced by the authors for the extensions of basic relations valid for bandlimited functions to larger function spaces. This approach can be regarded as a mathematical foundation of aliasing error analysis of many applications. Full article
(This article belongs to the Special Issue Information Theory Applied to Communications and Networking)
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