Sampling-reconstruction procedure with jitter of Gaussian processes

Abstract

The general approach of the statistical description of the sampling-reconstruction procedure (SRP) with jitter of Gaussian processes with an arbitrary number of samples is given. The analysis is based on the conditional mean rule. We consider the classification of all known mathematical models of jitter and describe the statistical average procedure in order to find the principal SRP characteristics with jitter: the reconstruction function and the error reconstruction function. We suggest the new interpretation of the reconstruction schemes on the basis of the kinetic equations for non-Markov processes. Some non-trivial examples are given