Sampling-reconstruction procedure of Gaussian processes with the mutual statistical connection between all couples of samples

This paper is devoted to the special statistical problem of the time synchronization in many modern digital systems. We investigate the Sampling-Reconstruction Procedure (SRP) of Gaussian processes when the instant times of samples are randomly changed. This effect is known as jitter. We restrict our interest to the joint jitter of any two samples. It means that the jitter effect is described by a two-dimensional probability density function (pdf). Two different pdf are used in this paper: Gaussian and the distribution obtained by McFadden. We get the error reconstruction functions for both samples. The influence of different parameters on the error reconstruction functions is investigated in detail. Some examples are presented and the results are compared when the parameter of the two jitter distributions are the same.