engleski

Some new generalizations of the Kotel'nikov - Shannon formula for stochastic signals

Regular and irregular derivative sampling formula of Whittaker type is developed for $L^\alpha(\Omega, \mathfrak F, \mathsf P)$ - valued stochastic processes, $\alpha \in [0, 2]$, such that has spectral representation with Leont'ev $[0, \pi q/2)$[ type kernal function. Weighted $L_2$ and almost sure sense derivatives are reconstructed and circular truncation error upper bounds are presented such that are by Pogany estimates of Weierstrass $\sigma$ - function realized.

Weierstrass $\sigma$ - function; Hayman's constants; circular truncation error upper bound; Kotel'nikov - Shannon sampling formula; weighted derivative of $L^\alpha$-processes; Piranashvili $\alpha$-processes

nije evidentirano