Statistical Characteristics of the Signal in the Presence of Modulating Noise

Statistical characteristics of narrow-band signal in the presence of modulating noise are considered, including case of determining the univariate density of signal distribution. The relationship between the characteristic function of instantaneous signal values and the probability distribution density (PDD) envelope with a uniform phase distribution law is determined. Expressions describing a PDD of instantaneous values of signal and additive noise under action of modulating noise are obtained. Cases where there is no and is functional relationship between amplitude and phase fluctuations have been analyzed. It is shown that with the law of phase distribution other than uniform at the interval $$[0,2\pi]$$ , the signal is a nonstationary random function tending to stationary at increasing the depth of phase distortions. With uniform phase distribution, the signal is a stationary random function. It is shown that in case of functionally connected amplitude-phase distortions, the PDD signal is described through statistical characteristics of its envelope.