engleski

Whittaker - type derivattive sampling reconstruction of stochastic $L^\alpha(\Omega)$ - processes

Mean square and almost sure Whittaker--type derivative sampling theorems are obtained for the class $L^\alpha( \Omega , {;\mathfrak F};, {;\mathsf P};) \ 0 \leq \alpha \le 2$ of stochastic processes having spectral representation, with the aid of the {; Weierstra\ss};$\sigma$ function. Functions of this class are represented by interpolatory series. The results are valid for harmonizable and stationary processes ($\alpha =2$) as well. The formul{; \ae}; are interpreted in the $\alpha$--mean sense and also in the almost sure ${;\mathsf P};$ sense when the initial signal function and its derivatives (up to some fixed order) are sampled at the points of the integer lattice ${; \mathbb Z}; ^2$. The circular truncation error is introduced and used in the truncation error analysis. Finally, sampling sum convergence rate is provided.

almost sure ${;;; \mathsf P};;; $ convergence; $\alpha$--mean convergence; $\alpha$--mean derivatives; Catalan constant; circular truncation error; derivative sampling; Karhunen--processes; $L^\alpha(\Omega; {;;; \mathfrak F};;;; {;;; \mathsf P};;; )$--processes

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