On Generalized Derivative Sampling Series Expansion

Zurab A. Piranashvili () and Tibor K. Pogány ()
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Zurab A. Piranashvili: Vladimir Chavchanidze Institute of Cybernetics, Georgian Technical University
Tibor K. Pogány: University of Rijeka, Faculty of Maritime Studies

Chapter Chapter 14 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 491-519 from Springer

Abstract: Abstract Master generalized sampling series expansion is presented for entire functions (signals) coming from a class whose members satisfy an extended exponential boundedness condition. Firstly, estimates are given for the remainder of Maclaurin series of those functions and consequent derivative sampling results are obtained and discussed. The established results are employed in evaluating the related remainder term of signals which occur in sampling series expansion of stochastic processes and random fields (not necessarily stationary or homogeneous) whose spectral kernel satisfies the relaxed exponential boundedness. The derived truncation error upper bounds enable to obtain mean-square master generalized derivative sampling series expansion formulae either for harmonizable Piranashvili-type stochastic processes or for random fields. Finally, being the sampling series convergence rate exponential, almost sure P sampling series expansion formulae are presented.

Keywords: Whittaker–Kotel’nikov–Shannon sampling theorem; Derivative sampling; Exponentially bounded signals; Entire functions; Truncation error upper bound; Harmonizable stochastic process; Piranashvili process; Karhunen process; Loève process; Weak sense stationary process; Mean-square convergence; Almost sure P convergence (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-15242-0_14

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DOI: 10.1007/978-3-030-15242-0_14

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