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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
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
