Applying factorization to increase the resolving ability of the parametric estimation of the power spectral density
DOI:
https://doi.org/10.30837/rt.2023.1.212.08Keywords:
random process, spectral power density, spectral resolution, factorization, autoregressive modelAbstract
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.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).