Title

A q-analogue of the Whittaker-Shannon-Kotelnikov sampling theorem

Authors

Authors

M. E. Ismail;A. I. Zayed

Comments

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Abbreviated Journal Title

Proc. Amer. Math. Soc.

Keywords

Shannon sampling theorem; band-limited and sinc functions; q-trigonometric series; basic hypergeometric functions; FOURIER; Mathematics, Applied; Mathematics

Abstract

The Whittaker-Shannon-Kotel'nikov (WSK) sampling theorem plays an important role not only in harmonic analysis and approximation theory, but also in communication engineering since it enables engineers to reconstruct analog signals from their samples at a discrete set of data points. The main aim of this paper is to derive a q-analogue of the Whittaker-Shannon-Kotel'nikov sampling theorem. The proof uses recent results in the theory of q-orthogonal polynomials and basic hypergeometric functions, in particular, new results on the addition theorems for q-exponential functions.

Journal Title

Proceedings of the American Mathematical Society

Volume

131

Issue/Number

12

Publication Date

1-1-2003

Document Type

Article

Language

English

First Page

3711

Last Page

3719

WOS Identifier

WOS:000184997200013

ISSN

0002-9939

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