Linear autoregressive processes with periodic structures as models of information signals




autoregressive process, periodic structure, recognition algorithm, information signal


Linear autoregressive processes with periodic structures are considered. Some properties of the random processes which could be applied for development of different information signals recognition algorithm are represented.


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

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).

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).

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).

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

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

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

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

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

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

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

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

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

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

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

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].

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

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).

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).

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.

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

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).

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).

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

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

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

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

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

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

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





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