Modeling and Analysis the Characteristics of an Ensemble of Signal Implementations, Distorted by Fluctuation Multiplicative Noise

The relationship of the structure of the signal distorted by the noise with the structure of the undistorted signal and the characteristics of the noise modulation function is considered. An expression is obtained for a signal distorted by a deterministic multiplicative noise, in which the noise component is a separate term. It is shown that for an ensemble of realizations of a signal distorted by a stationary fluctuation multiplicative noise, the mathematical expectation of this signal can be considered as its undistorted part; there is also an noise component in the ensemble. The relative level of the undistorted part of the signal is determined by the joint distribution function of the changes in the amplitude and phase at coinciding time instants. It is shown that the fluctuation of the function of the interfering component is a complex envelope of the interfering component of the harmonic signal. Expressions are obtained for the correlation function of the interfering one leaving for a constant and random value of the initial phase of the signal. It is shown that the averaged correlation function of the noise component of the signal distorted by multiplicative noise can be expressed in terms of the autocorrelation function of the signal and the correlation function of noise modulation fluctuations. It is also shown that the energy spectrum of the interfering component is wider than the energy spectrum of the undistorted signal. The main characteristics of the considered ensemble of signal realizations are the relative level of the undistorted part of the signal and the correlation function or energy spectrum of the interfering component, which characterize fluctuations of the distorted signal.