Covariance characteristics of narrowband periodically non-stationary random signals

2019;
: pp. 276–288
https://doi.org/10.23939/mmc2019.02.276
Received: September 05, 2019
Revised: October 29, 2019
Accepted: November 01, 2019

Mathematical Modeling and Computing, Vol. 6, No. 2, pp. 276–288 (2019)

1
Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine, Laboratory of vibration-based diagnosis; UTP University of Sciences and Technology, Institute of Telecommunication and Computer Science
2
Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine, Laboratory of vibration-based diagnosis; Lviv Polytechnic National University, Department of Applied Mathematics
3
Karpenko Physico-Mechanical Institute of National Academy of Sciences of Ukraine, Laboratory of vibration-based diagnosis; Lviv Polytechnic National University, Department of Applied Mathematics

Hilbert transform of a narrowband periodically non-stationary random signal (PNRS) is considered.  The relations for the covariance components of PNRS and its Hilbert transform are obtained.  The dependencies of the covariance properties of Hilbert transform on covariance damping coefficients of modulating processes are analyzed on the basis of the simulated realizations.

  1. Rytov S. M., Kravtsov Yu. A., Tatarskii V. I.  Principles of Statistical Radiophysics 1 --- Elements of Random Process Theory.  Berlin, Heidelberg, Springer--Verlag (1987).
  2. Deutsch R.  Nonlinear transformations of nonlinear Processes.  New York, Prentice Hall, Englewood Cliffs (1962).
  3. Tihonov V. I.  Nelinejnye preobrazovanija sluchajnyh processov.  Moskva, Radio i Sviaz  (1986), (in Russian).
  4. Levin B. R.  Teoreticheskie osnovy statisticheskoj radiotehniki.  Moskva, Sovetskoe radio (1974), (in Russian).
  5. Papoulis A.  Random modulation: A review.  IEEE Transactions on Acoustics, Speech, and Signal Processing. 31 (1), 96--105 (1983).
  6. Garder W. A.  Introduction to random processes with application to signal and systems.  New York, Macmillan Pub. Co (1985).
  7. Bendat J. S., Piersol A. G.  Random data: analysis and measurement procedures.  Wiley (2010).
  8. Gabor D.  Theory of communication.  Journal of the Institution of Electrical Engineers -- Part III: Radio and Communication Engineering. 93 (26), 429--441 (1946).
  9. Oppenheim A. V., Schafer R. W.  Digital signal processing.  New York, Prentice Hall (1975).
  10. Randall R. B., Antoni I., Chobsaard S.  The relation between spectral correlation and envelope analysis.  Mechanical Systems and Signal Processing. 15 (5), 945--962 (2001).
  11. Javorskyi I., Kravets I., Matsko I., Yuzefovych R.  Periodically correlated random processes: Application in early diagnostics of mechanical systems.  Mechanical Systems and Signal Processing. 83, 406--438 (2017).
  12. Javorskyi I.  Mathematical models and analisys of stochastic oscillations.  Lviv, Karpenko Physico-Mechanical Institute (2013), (in Ukraine).
  13. Feldman M.  Hilbert transform applications in mechanical vibration.  John Wiley (2011).
  14. Rozhkow V.  Metody verojatnostnogo analiza okeanologicheskih processov.  Leningrad, Gidrometeoizdat (1974), (in Russian).
  15. Dragan Y., Rozhkow V., Javorskyj I.  Metody verojatnostnogo analiza ritmiki okeanologicheskih processov.  Leningrad, Gidrometeoizdat (1987), (in Russian).
  16. Bjorno L.  Underwater acoustics and aignal processing.  London, D. Reidel Publishing (1981).
  17. Vainshtein L. A., Vakman D. E.  Frequency division in the theory of oscillations and waves.  Moscow, Nauka (1983), (in Russian).
  18. Cramer H.,  Leadbetter M. R.  Stationary and related stochastic processes: sample function properties and their applications.  New York, John Wiley & Sons (1967).
  19. Bedrosian E.   A product theorem for Hilbert transform.  Proceedings of the IEEE. 51, 868--869 (1963).
  20. Javorskyi I., Yuzefovych R., Kurapov P.  Periodically non-stationary analytic signals and their properties.  2018 IEEE 13th International Scientific and Technical Conference on Computer Sciences and Information Technologies (CSIT). 191--194 (2018).