A -analogue of the Whittaker-Shannon-Kotel'nikov sampling theorem

Authors:
Mourad E. Ismail and Ahmed I. Zayed

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3711-3719

MSC (2000):
Primary 33B10, 33D15; Secondary 42C15, 94A11

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

Published electronically:
July 17, 2003

MathSciNet review:
1998178

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Abstract | References | Similar Articles | Additional Information

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 -analogue of the Whittaker-Shannon-Kotel'nikov sampling theorem. The proof uses recent results in the theory of -orthogonal polynomials and basic hypergeometric functions, in particular, new results on the addition theorems for -exponential functions.

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Additional Information

**Mourad E. Ismail**

Affiliation:
Department of Mathematics, University of Central Florida, Orlando, Florida 32816

Email:
ismail@math.usf.edu

**Ahmed I. Zayed**

Affiliation:
Department of Mathematical Sciences, DePaul University, Chicago, Illinois, 60614

Email:
azayed@math.depaul.edu

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

Keywords:
Shannon sampling theorem,
band-limited and sinc functions,
$q$-trigonometric series,
basic hypergeometric functions

Received by editor(s):
February 19, 2002

Published electronically:
July 17, 2003

Additional Notes:
Research partially supported by NSF grant DMS 99-70865 and the Liu Bie Ju Centre of Mathematical Sciences

Communicated by:
David R. Larson

Article copyright:
© Copyright 2003
American Mathematical Society