Skip to main content
Log in

Linear autoregressive processes with periodic structures as models of information signals

  • Published:
Radioelectronics and Communications Systems Aims and scope Submit manuscript

Abstract

Linear autoregressive processes with periodic structures have been considered. Certain properties of such processes that can be used in developing the recognition algorithms of different types of information signals were also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. L. Marple, Jr., Digital Spectral Analysis with Applications (Prentice Hall, 1987; Mir, Moscow, 1990).

  2. V. I. Koshelev and V. G. Andreev, “Synthesis of ARMA Models of Echo Signals,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 36(7), 8 (1993); Radioelectron. Commun. Syst. 36 (7), 6 (1993).

    Google Scholar 

  3. V. N. Zvarich and B. G. Marchenko, “The Method of Determining Characteristic Functions of the Generating Processes for Linear Autoregression Processes,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 42(7), 64 (1999); Radioelectron. Commun. Syst. 42 (7), 58 (1999).

    Google Scholar 

  4. V. N. Zvarich and B. G. Marchenko, “Characteristic Function of the Generating Process in the Model of Stationary Linear AR-gamma Process,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 45(8), 12 (2002); Radioelectron. Commun. Syst. 45 (8), 10 (2002).

    Google Scholar 

  5. B. G. Quinn, “Statistical Methods of Spectrum Change Detection,” Digital Signal Processing 16, 588 (2006).

    Article  Google Scholar 

  6. B. G. Quinn, “Recent Advances in Rapid Frequency Estimation,” Digital Signal Processing 19, 942 (2009).

    Article  Google Scholar 

  7. S. Nakamori, “Design of Extended Recursive Wiener Fixed-Point Smoother and Filter in Discrete-Time Stochastic Systems,” Digital Signal Processing 17, 360 (2007).

    Article  Google Scholar 

  8. E. E. Slutskii, Selected Works. Probability Theory. Mathematical Statistics (Izdat. AN SSSR, Moscow, 1970) [in Russian].

    Google Scholar 

  9. L. I. Gudzenko, “On Periodicity of Nonstationary Processes,” Radiotekh. Elektron. 4, No. 6, 1062 (1959).

    Google Scholar 

  10. E. G. Gladyshev, “Periodic and almost Periodic Continuous Time Correlated Random Processes,” Probabilities Theory and Its Application 8, No. 2, 184 (1963).

    Article  Google Scholar 

  11. M. Loev, Probability Theory (Moscow, 1962) [in Russian].

  12. R. H. Jones and W. M. Brelsford, “Time series with periodic structure,” Biometrika 54, No. 3–4, 403 (1967).

    MathSciNet  MATH  Google Scholar 

  13. H. Ogura, “Spectral Representation of a Periodic Nonstationary Random Process,” IEEE Trans. Inf. Theory IT-17, No. 2, 143 (1971).

    Article  MathSciNet  Google Scholar 

  14. W. A. Gardner and L. E. Franks, “Characterization of Cyclostationary Random Signal Processes,” IEEE Trans. Inf. Theory IT-21, No. 1, 5 (1975).

    Google Scholar 

  15. M. Pagano, “On Periodic and Multiple Autoregressions,” Annals of Statistics 6, No. 6, 1310 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  16. M. V. Myslovich, N. V. Priimak, and L. N. Shcherbak, Periodically Correlated Random Processes in Problems of Acoustic Data Processing (Znanie, Kiev, 1980) [in Russian].

    Google Scholar 

  17. I. N. Yavorskii, “Statistical Analysis of Periodically Correlated Random Processes,” Radiotekh. Elektron. 30, No. 6, 1096 (1986).

    Google Scholar 

  18. V. Zvaritch, M. Myslovitch, and B. Martchenko, “The Model of Random Periodic Information Signals on the White Noise Bases,” Appl. Math. Lett. 8, No. 3, 87 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  19. V. N. Zvarich, M. V. Myslovich, and B. G. Marchenko, “Stochastically Periodic Random Processes as Models of Information Signals,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 38(1), 46 (1995); Radioelectron. Commun. Syst. 38 (1), 38 (1995).

    Google Scholar 

  20. V. N. Zvarich and B. G. Marchenko, “Linear Autoregression Processes with Periodic Structures,” in Proc. of 3rd Int. Conf. AVIA-2001, April 24–26, 2001, Kyiv, Ukraine (Kyiv, 2001), Vol. 3, pp. 8.75–8.78.

    Google Scholar 

  21. B. G. Marchenko, “Linear Periodic Processes,” in Trans. of the Institute of Electrodynamics (Kyiv, 1999), pp. 172–185.

  22. V. N. Zvarich and B. G. Marchenko, “Linear Autoregression Processes in Problems of Vibration-Based Diagnostics of Electric Machine Assemblies,” Tekhnicheskaya Diagnostika i Nerazrushayushchii Kontrol’, No. 1, 45 (1996).

  23. D. Labarre, E. Grivel, Y. Bersonmie, et al., “Consistent estimation of autoregressive parameters from noisy observations based on two interacting Kalman filters,” Signal Processing 86, 2863 (2006).

    Article  MATH  Google Scholar 

  24. J. Antony, F. Guillet, M. Badooni, and F. Bonvardot, “Blind Separation of Convolved Cyclostationary Process,” Signal Processing 85, 51 (2005).

    Article  Google Scholar 

  25. A. Kowalski and D. Szynal, “An Optimal Prediction in General ARMA Models,” J. Multivariate Analysis 34, 14 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  26. H. Hurd, A. Makagon, and A. G. Miamee, “On AR(1) models with periodic and almost periodic coefficient,” Stoch. Process. Applications 100, 167 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  27. A. G. Miamee and S. Talebi, “On PC Solution of PARMA (p, q) models,” Probab. Math. Statistics 25, 279 (2005).

    MathSciNet  MATH  Google Scholar 

  28. A. M. Reuven and A. J. Weiss, “Direct Position Determination of Cyclostationary Signals,” Signal Processing 89, 360 (2009).

    Article  Google Scholar 

  29. K. Sabri, M. E. Badaoui, F. Guillet, et al., “Cyclostationary Modeling of Ground Reaction Force Signals,” Signal Processing 90, 1146 (2010).

    Article  MATH  Google Scholar 

  30. I. Javorskyj, I. Isaev, J. Maevski, and R. Yuzefovich, “Component Covariance Analysis for Periodically Correlated Random Processes,” Signal Processing 90, 1083 (2010).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © V.N. Zvarich B.G. Marchenko, 2011, published in Izv. Vyssh. Uchebn. Zaved., Radioelektron., 2011, Vol. 54, No. 7, pp. 25–30.

About this article

Cite this article

Zvarich, V.N., Marchenko, B.G. Linear autoregressive processes with periodic structures as models of information signals. Radioelectron.Commun.Syst. 54, 367–372 (2011). https://doi.org/10.3103/S0735272711070041

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0735272711070041

Keywords

Navigation