Title

A Q-Analogue Of The Whittaker-Shannon-Kotel'Nikov Sampling Theorem

Keywords

Band-limited and sinc functions; Basic hypergeometric functions; q-trigonometric series; Shannon sampling theorem

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.

Publication Date

12-1-2003

Publication Title

Proceedings of the American Mathematical Society

Volume

131

Issue

12

Number of Pages

3711-3719

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-03-07208-3

Socpus ID

0344497386 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0344497386

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