Analysis of Relations between the Characteristics of the Ensemble of Signal Implementations Distorted by Fluctuation Modulating Noise and Individual Realizations of this Signal

The analysis of the ratio between the undistorted part of the signal in a separate realization and in each signal ensemble is carried out. It is shown that the mathematical expectation of the power level of the undistorted part of the signal in individual realizations is the closer to the power level of the undistorted part of the signal for an ensemble of implementation, the shorter the correlation time of fluctuations of the noise modulation function as compared to the signal duration. A relation is obtained for estimating the variance of the time correlation function of individual realizations of a signal. An expression is obtained for estimating the difference between the time correlation function of individual realizations of a signal and the correlation function that characterizes the ensemble of such signals. The condition is determined under which the relative value of the variance of the correlation function of individual realizations is sufficiently small and the time correlation function found for a separate realization of a signal is close to the correlation function obtained for an ensemble of such signals. It is shown that the characteristics defined for the ensemble of implementations give correct and complete information of the distortions of individual realizations of such a signal in cases where the distortion correlation time is much less than the signal duration. At the same time, in these cases, it is possible to draw a conclusion the characteristics of the entire ensemble of signals from a single realization.