Applying factorization to increase the resolving ability of the parametric estimation of the power spectral density

Authors

DOI:

https://doi.org/10.30837/rt.2023.1.212.08

Keywords:

random process, spectral power density, spectral resolution, factorization, autoregressive model

Abstract

We consider a possibility of the factorization of parametric spectral power density (PSM) estimation of a random process based on autoregressive linear prediction model to increase the spectrum resolution. Factorization refers to the decomposition of the multimode PSM into simpler single-mode components. Factorization makes it possible not only to decompose a complex multimode PSM into simple single-mode components, but also to analyze more accurately the low-, medium- and high-frequency components of the SPM of a random process. The main attention is paid to the study of the problem of increasing the resolving power of SPM estimation by its factorization by the Yule-Walker and Berg method.

References

G. Box, G. Jenkins, G.C. Reinsel. Time Series Analysis, Forecasting and Control, 4th ed. Hoboken. USA : Wiley, 2008.

Brockwell P.J., Davis R.A. Introduction to Time Series and Forecasting. Springer, 2002.

Kitagawa G., Gersch W. Smoothness Priors Analysis of Time Series. New York : Springer, 1996.

Drubin J., Koopman S. Time Series Analysis by State Space Methods. Oxford : Oxford Univ. Press, 2008.

Hyndman R., Koehler A., Snyde R., Grose S. A state space framework for automatic forecasting using exponential smoothing methods // Int. J. Forecast. 2002. Vol. 18, no. 3. Pp. 439 – 454.

Young P.C. Stochastic, dynamic modelling and signal processing: Time variable and state dependent parameter estimation // Nonlinear and Nonstationary Signal Processing. Cambridge : Cambridge Univ. Press, 2000. Рp. 41 – 114.

Young P.C. Recursive estimation and time series analysis // Introduction for the Student and Practioner. Berlin : Springer-Verlag, 2011.

Tong H. Nonlinear Time Series: A Dynamical Systems Approach. Oxford : Oxford Univ. Press, 1990.

Ozaki T. Non-linear time series models for non-linear random vibrations // J. Appl. Probabil. 1980. Vol. 17. Рp. 84–93.

Haggan V., Ozaki T. Modeling nonlinear random vibrations using an amplitude-dependent autoregressive time series model // Biometrika. 1981. Vol. 68. Рp. 189 – 196.

Priestley M.B. State dependent models: A general approach to nonlinear time series analysis // J. Time Series Anal. 1980. Vol. 1, no 1. Рp. 57 – 71.

Chen R., Tsay R.S. Functional-coefficient autoregressive models // Amer. Statist. Assoc. 1993. Vol. 88, no. 21. Рp. 298 – 308.

Tykhonov V.A., Kudriavtseva N.V., Chmelar P. Factorization of speech signals parametric spectra using multiplicative linear prediction models // Proceedings Elmar. 57th International Symposium ELMAR-2015, Zadar, 28 – 30 September. 2015. Рр. 124 – 130.

Кармалита В.А. Цифровая обработка случайных колебаний. Москва : Мир, 1989.

Карташов В.М., Олейников В.Н., Тихонов В.А. и др. Обработка сигналов в радиоэлектронных систе-мах дистанционного мониторинга атмосферы. Харьков : Компания СМИТ, 2014.

Марпл мл. С.Л. Цифровой спектральный анализ и его приложения. Москва : Мир, 1990.

Тихонов В.А., Русановский Д.Е., Тихонов Д.В. Генерирование узкополосных имитационных случайных процессов // Радиоэлектроника и информатика. 1999. №4. С. 83 – 85.

Омельченко В.А., Безрук В.М., Коваленко Н.П. Распознавание заданных радиосигналов при наличии неизвестных сигналов на основе авторегрессионной модели // Радиотехника. 2001. Вып. 123. С. 195 – 199.

Published

2023-03-28

How to Cite

Tikhonov, V., & Bezruk, V. (2023). Applying factorization to increase the resolving ability of the parametric estimation of the power spectral density. Radiotekhnika, 1(212), 90–101. https://doi.org/10.30837/rt.2023.1.212.08

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Articles