Naslov
Bessel–Sampling Restoration of Stochastic Signals

Autori
Poganj, Tibor

Izvornik
Acta Polytechnica Hungarica (1785-8860) 10 (2013), 7; 7-19

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Almost sure convergence ; Bessel functions of the first and second kind ; Correlation function ; Bessel sampling ; Harmonizable stochastic processes

Sažetak
The main aim of this article is to establish sampling series restoration formulae for a class of stochastic L2-processes which correlation function possesses integral representation close to a Hankel-type transform which kernel is either Bessel function of the first and second kind Jn ; Yn respectively. The results obtained belong to the class of irregular sampling formulae and present a stochastic setting counterpart of certain older results by Zayed [25] and of recent results by Knockaert [13] for J–Bessel sampling and of currently established Y– Bessel sampling results by Jankov Maširević et al. [7]. The approach is twofold, we consider sampling series expansion approximation in the mean–square (or L2) sense and also in the almost sure (or with the probability 1) sense. The main derivation tools are the Piranashvili’s extension of the famous Karhunen–Cramer theorem on the integral representation of the correlation functions and the same fashion integral expression for the initial stochastic process itself, a set of integral representation formulae for the Bessel functions of the first and second kind Jn ; Yn and various properties of Bessel and modified Bessel functions which lead to the so–called Bessel–sampling when the sampling nodes of the initial signal function coincide with a set of zeros of different cylinder functions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Tehnologija prometa i transport

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