A Q-Analogue Of The Whittaker-Shannon-Kotel'Nikov Sampling Theorem
Band-limited and sinc functions; Basic hypergeometric functions; q-trigonometric series; Shannon sampling theorem
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.
Proceedings of the American Mathematical Society
Number of Pages
Article; Proceedings Paper
Source API URL
Ismail, Mourad E. and Zayed, Ahmed I., "A Q-Analogue Of The Whittaker-Shannon-Kotel'Nikov Sampling Theorem" (2003). Scopus Export 2000s. 1487.