STATISTICAL CHARACTERISTICS OF THE SIGNAL IN THE PRESENCE OF MODULATING NOISE
V. M. Artyushenko1, V. I. Volovach2
1Leonov Moscow Region University of Technology, Korolev, Moscow Region, Russia
2Volga Region State University of Service, Tol'yatti, Russia
Keywords: multiplicative (modulating) noise, narrow-band useful signal, amplitude distortions, phase distortions, functional relationship, characteristic function
Abstract
Statistical characteristics of a narrow-band signal in the presence of modulating noise are considered, including the case of determination of the univariate density of the signal distribution. The relationship between the characteristic function of the instantaneous signal values and the probability distribution density (PDD) envelope with a uniform phase distribution law is determined. Expressions describing the PDD of the instantaneous values of the signal and additive noise under the action of modulating noise are obtained. Cases without and with a functional relationship between the amplitude and phase fluctuations are analyzed. With the phase distribution law other than uniform on the interval [0, 2π], the signal is demonstrated to be a non-stationary random function tending to stationary as the depth of phase distortions increases. With a uniform phase distribution, the signal is a stationary random function. In the case of functionally connected amplitude-phase distortions, the PDD signal is described through the statistical characteristics of its envelope.
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