Whittaker-type derivative sampling reconstruction of stochastic Lα(Ω)-processes

摘要

Mean square and almost sure Whittaker-type derivative sampling theorems are obtained for the class Lα(Ω,F,P); 0 ⩽ α ⩽ 2 of stochastic processes having spectral representation, with the aid of the Weierstraß σ function. Functions of this class are represented by interpolatory series. The results are valid for harmonizable and stationary processes (α = 2) as well. The formulæ are interpreted in the α-mean sense and also in the almost sure P sense when the initial signal function and its derivatives (up to some fixed order) are sampled at the points of the integer lattice Z2. The circular truncation error is introduced and used in the truncation error analysis. Finally, sampling sum convergence rate is provided.