Stationary random processes interpolation on the basis of atomic functions

The methods of restoration of stochastic processes on the discrete samples on the basis of atomic functions are considered. A comparison of the proposed methods with the optimal criterion of minimum mean square error recovery is done. Problems of sampling and interpolation of continuous signals are of great importance in the theory of random processes. Problems of estimates replacing discrete processes on continuous errors arise as well as optimizing the characteristics of the interpolating filters according to the criterion of minimum mean square error (RMS) interpolation when s sampling increment is selected. The purpose of work is to study methods of interpolation of stochastic processes (SSP) on the basis of AF and compared them with the difficult to do on practice the best method. On the first stage the general relations for the correlation function, energy spectrum and the dispersion error of interpolation of arbitrary SSP are considered. We find the optimal parameters of the restoring filter according to the criterion of minimum RMS interpolation. On the second stage for a particular random process the various schemes of interpolation (step, linear and sinc interpolation) compared with the optimum are analized. Particular attention is given to the method of interpolation with the help of families of atomic functions