Statistical Characteristics of the Signal Distribution at the output of the Linear Filter in the Presence of Fluctuating Modulating Noise

The statistical characteristics of the signal distribution, which is under the influence of fluctuating modulating noise, at the output of the linear filter are given. Required analysis was performed for linear circuits with integral type transformations. It has been shown that in this case the probability distribution density of random functions is conveniently represented by an Edgeworth row. Analysis has shown that the average value of the output signal oscillates with some carrier frequency, and the dispersion has both axing and non-oscillating components. The convergence of output signal distribution is estimated for two typical cases. It is noted that the increase in the number of independent summing sum series converges to the normal distribution of prime at any finite values of coefficients of the named series. The results are obtained for the first initial moments of the signal, and their relationship with the coefficients of the investigated series is shown for a number of specific cases. The accuracy of approximation of the law of signal distribution distorted by random modules-steering noise was quantified. It is shown that under general assumptions about distribution of amplitude and phase distortions, the law of distribution of a signal distorted by stationary modules-steering interference can be adopted with sufficient accuracy by normal law with non-oscillating second moment only when a number of conditions are met. Example is given and analysis is carried out, including graphic analysis, of conditions of convergence of said law of signal distribution at output of linear circuit to normal distribution with oscillating second moment. In particular, it has been shown that with small phase distortions, the law of signal distribution approaches normal rather quickly with an oscillating second moment.