Sampling and \(\Pi\)-sampling expansions (Q1592949)
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scientific article; zbMATH DE number 1553301
| Language | Label | Description | Also known as |
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| English | Sampling and \(\Pi\)-sampling expansions |
scientific article; zbMATH DE number 1553301 |
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Sampling and \(\Pi\)-sampling expansions (English)
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27 March 2001
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Using the hyperfinite representation of functions and generalized functions, this paper develops a rigorous version of the so-called ``delta method'' approach to sampling theory. (For a derivation of the delta method using standard analysis, see \textit{M. Z. Nashed} and \textit{G. G. Walter} [Math. Control Signals Syst. 4, 363-390 (1991; Zbl 0734.46019)].) The nonstandard analysis approach adopted by the paper under review yields a slightly more general version of the classical WKS sampling theorem for band-limited functions.
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sampling expansions
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WKS sampling theorem
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nonstandard analysis
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hyperfinite sums
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