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

    Authors

    M. E. Ismail;A. I. Zayed

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    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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