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The chapter describes the representations of the mean and correlation functions

of the PNVP in the form of Fourier series. It was noted that the coefficients of these

series characterize the stochastic amplitude and phase modulation of the carrier

harmonics of the PNRP. The narrow-band PNRP and the properties of its Hilbert

transform are also considered. It is noted the difference between correlation and

spectral characteristics of quadrature components in stationary and non-stationary

cases. A brief analysis of methods for detecting hidden periodicities, which are

described by PNRP, as well as methods for evaluating their characteristics, is given.

The Second Chapter is devoted to studying of the correlation-spectral properties

of the signal described by the Rice model, whose quadrature components are high-

frequency stationary joined random processes. The properties of the Hilbert transform

of such a signal were analyzed, and the formulas were obtained, that related the

characteristics of the quadrature of the signal and the quadrature of its Hilbert

transform. It is shown that the application of the Hilbert transform does not change

the correlation-spectral structure of the signal. It is proved that the analytical signal is

a complex-valued PNRP and the formulas for its correlation components are

introduced. It is shown that its variance is equal to twice the variance of the raw

signal. For the case when the modulation is narrow-band, a representation in the form

of a sum of stationary high-frequency components is obtained. It is shown that these

components are jointly PNRP. Algorithms for the extraction of quadratures of the

high-frequency narrow-band modulations are substantiated. Analysis of which makes

it possible to investigate the regularities of high-frequency modulation in more

details. An indicator for characterizing the state of contact surfaces is proposed, the

formula of which involves both – changes in the average power of stochastic

oscillations as well as the total amplitude of harmonics of its temporal changes. The

calculation results are given for each stage of experiment in the form of graphic

dependencies, diagrams, tables, and their comparison is presented explained also.

In the Third Chapter, the obtained theoretical results are used to analyze the

condition of the rotating unit of the lifting mechanism of the port crane. The signal

analysis was carried out separately in the low-frequency and high-frequency bands. It
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