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Lecturer(s)
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Tuček Jiří, doc. Mgr. Ph.D.
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Pidanič Jan, doc. Ing. Ph.D.
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Marek Jaroslav, Mgr. Ph.D.
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Course content
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1. Random phenomena: Random experiment. Elementary and random phenomenon. Algebra of random phenomena 2. Probability: statistical definition of probability, conditional probability, independent phenomena, complete probability theorem. 3. Random variable, random vector: Distribution function. Random variables and vectors with discrete and continuous probability distributions. Independence of random variables. Conditional probability distribution 4. Numerical characteristics of random variables: mean, variance, standard deviation and their properties. General and central moments. Covariance and correlation coefficient 5. Random processes and signals: definition of random processes and signals and characteristics of random signals (statistical character, empirical character.), Stationary and ergodic signals 6. Spectral properties of random signals, the transmission of a random signal by linear system in time and frequency domain 7. Decomposition of a random signal: definition (examples of decomposition of determined signals), orthogonal decomposition of random signals, properties of the vector of decomposition coefficients, or uncorrelated decomposition 8. White Gaussian noise (WGN): definition, properties, amplitude and phase distribution, harm characteristics. signal with WGN 9. Band random signals: definition, Hilbert signal, complex envelope and phase of random band signal, orthogonal and polar representations of random band signal 10. Estimation of random signal characteristics, estimation criteria, methods of estimation of correlation and covariance functions and matrices (direct estimation, estimation in the frequency domain, estimation based on power spectrum) 11. Model of random ARMA signals, methods of estimation of model parameters 12. Restoration of random signals, optimal LMS restoration of signals, identification of random signals in noise (cumulation methods, correlation analysis) 13. Spectral analysis of deterministic and stochastic signals
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Learning activities and teaching methods
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unspecified, Monologic (reading, lecture, briefing)
- Participation in classes
- 150 hours per semester
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Learning outcomes
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The course follows the courses Mathematics 1, Mathematics 2 and Fundamentals of Probability Theory and Mathematical Statistics. The aim of the course is to expand students' knowledge in the field of probability theory and mathematical statistics. The theoretical knowledge will be required for the processing of random signals in electronic communication and radar systems. Emphasis is placed on methods for estimating the characteristics of random signals, restoring random signals and identifying the parameters of their models.
By studying the course, the student will gain deeper knowledge about the expression, characteristics, analysis and processing of random signals used in the field of communication and radar systems.
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Prerequisites
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Mathematical calculus at the technical university graduates level. Knowledge of SW Matlab.
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Assessment methods and criteria
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Oral examination, Written examination
Prerequisite for successful completion of the course is a good basic knowledge of signal processing. In addition to visits to lectures and exercises, the study also includes the elaboration of a protocol for solving individual problems in the field of digital signal processing assigned during the semester.
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Recommended literature
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Heiberger, Richard M. a Burt Holland. Statistical Analysis and Data Display. 2nd Edition.. Springer New York, 2015. ISBN 978-1-4939-2122-5.
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Jan, Jiří. Číslicová filtrace, analýza a restaurace signálů. Brno: VUTIUM, 2002. ISBN 80-214-1558-4.
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Kay Steven M. Fundamentals of statistical signal processing: estimation theory.. Prentice Hall PTR, 1993. ISBN 01-334-5711-7.
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Kubáčková Ludmila. Náhodná funkce a jejich aplikace. Olomouc: Univerzita Palackého, 1996. ISBN 80-7067-6566.
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Souček Eduard. Základy pravděpodobnosti a statistiky, 3. vydání. Pardubice: Univerzita Pardubice, 2008. ISBN 978-80-7395-142-9.
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