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Lecturer(s)
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Kubalčík Marek, doc. Ing. Ph.D.
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Course content
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1. Basic terms from the areas of identification and modelling, random phenomena, random variables, signals and processes 2. Basic statistical characteristics of random processes -mean value, variance, standard deviation, standard quadartic deviation, distribution function, probability density. 3. Basic statistical characteristics of random processes- covariance, covariance matrix, correlation coefficent. 4. Stationarity and ergodicity of random processes 5. Autocorrelation and cross-correlation functions, covariance and cross-covariance functions. 6. Power spectral density, mutual power spectral density. 7. Passing of a random signal through a linear system. 9. Spectral transformation of a random signal during passing a linear system, spectral analysis. 10. Testing signals - white noise, pseudorandom signals, (PRBS- pseudorandom binary sequence). 11. Description of random signals by regression models AR, MA, ARMA. 12. Regression models of systems with influence of random signals - ARX, ARMAX, BJ, OE, ARARX, FIR 13. Parameter estimation of regression models using the explicit least squares method. 14. Parameter estimation of regression models using the recursive least squares method.
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Learning activities and teaching methods
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Lecturing, Monologic (Exposition, lecture, briefing), Exercises on PC, Individual work of students
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| prerequisite |
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| Knowledge |
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| Knowledge of basic parts od mathematical statistics, knowledge of basics of linear systems theory |
| Knowledge of basic parts od mathematical statistics, knowledge of basics of linear systems theory |
| learning outcomes |
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| explain basic terms from the theory of random processes |
| explain basic terms from the theory of random processes |
| explain classification of models used for description of random signals |
| explain classification of models used for description of random signals |
| describe basic statistical charakteristics of random processes |
| describe basic statistical charakteristics of random processes |
| describe utilization of random signals |
| describe utilization of random signals |
| characterize models of time series |
| characterize models of time series |
| Skills |
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| compute of statistical characteristics of random signals in time domain |
| compute of statistical characteristics of random signals in time domain |
| compute of statistical characteristics of random signals in frequency domain |
| compute of statistical characteristics of random signals in frequency domain |
| use statistical characteristics of random signals for correlation and spectral analysis |
| use statistical characteristics of random signals for correlation and spectral analysis |
| perform basic time series analysis |
| perform basic time series analysis |
| estimate of time series model parameters using regression methods |
| estimate of time series model parameters using regression methods |
| teaching methods |
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| Knowledge |
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| Individual work of students |
| Individual work of students |
| Monologic (Exposition, lecture, briefing) |
| Lecturing |
| Lecturing |
| Exercises on PC |
| Monologic (Exposition, lecture, briefing) |
| Exercises on PC |
| assessment methods |
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| Composite examination (Written part + oral part) |
| Composite examination (Written part + oral part) |
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Recommended literature
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Bobál, V. Identifikace systémů. Univerzita Tomáše Bati ve Zlíně, Academia centrum, 2009. ISBN 978-80-7318-888-7.
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Kubalčík, Marek. Cvičení z předmětu Identifikace systémů. Vyd. 1. Zlín : Univerzita Tomáše Bati ve Zlíně, 2006. ISBN 80-7318-497-4.
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Nelles, O. Nonlinear System Identification. Springer_Verlag Berlin, 2001. ISBN 3-540-67369-5.
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Noskievič, Petr. Modelování a identifikace systémů. Ostrava : Montanex, 1999. ISBN 80-7225-030-2.
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Oppenheim, Alan V. Signals & systems. 2nd ed. Upper Saddle River : Prentice Hall, 1997. ISBN 0-13-814757-4.
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Zaplatílek, Karel. MATLAB : začínáme se signály. 1. vyd. Praha : BEN - technická literatura, 2006. ISBN 80-7300-200-0.
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