Czech

Not applicable.

Students after completing the course should be able to solve problems associated with verification and testing assumptions and properties of the investigated phenomena and data files in the telecommunications field.
The student is able to:
- Quantifying the probability of the event
- Distinguishing between the random variables and describe their characteristics
- To test the hypothesis by parametric and non-parametric way
- Describe the probability density by Gaussian mixture models
- Estimating the shape of the spectrum and identify the spectral components
- Identify and test the presence of a signal in noise

Successful completion of courses, BMA1, BMA2, eventually KMA1, KMA2 are requested.
A student who register the course should be able to:
- To compose a simple program in Matlab
- Practicing a mathematical calculation procedures

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Requirements for completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every.

Lectures:
1. Introduction to the subject, probability theory, dependent and independent experiments, conditional probability.
2. The definition and the type of random variables, the characteristics of random variables, an entropy.
3. Multinomial random variables.
4. Functions of continuous random variables.
5. The central limit theorem and the law of large numbers.
6. Introduction to the theory of statistics, point and interval estimation, confidence intervals
7. Hypothesis testing, the parametric and the nonparametric approach.
8. Gaussian mixed models.
9. Random processes (stationarity, ergodicity of stationary processes, energy spectrum, Gaussian process).
10. Transformation of random processes.
11. Orthogonal transformation, Karhunen-Loev transformation, PCA.
12. Spectrum estimation techniques (parametric and nonparametric methods).
13. Detection of hidden signals in noises

Exercise on the PC:
1. The problems of probability theory (dependent and independent events, repeated events, conditional probability).
2. Tasks on the distribution of random variables, calculation of the characteristics of random variables and calculation of entropy.
3. Transformation of random variables, the generalized Rayleigh probability distribution, the probability distribution of the sum of random variables with normal distribution and the distribution of chi-square and uniform.
4. Calculation of confidence intervals, the derivation of system reliability.
5. Testing the significance of the estimates, the parametric and the nonparametric approach.
6. Random processes, stationarity testing.
7. Written exam I.
8. Examples of Gaussian mixed models.
9. Examples of transformations of random processes.
10. Examples of orthogonal transformation.
11. Application of estimation methods on simulated signal spectrum.
12. Calculation and testing for the presence of signal in the channel, goodness of fit tests, examples of detectors.
13. Written exam II.

Not applicable.

The proposed structure of the subject focuses on the use of selected mathematical techniques in modern communication signal processing and wireless communication theory. The goal is to present students with master's degree program Electronics and Communication Engineering specialized mathematical apparatus, which is essential to understanding the principles of modern wireless communications.

Evaluation of activities is specified by a regulation, which is issued by the lecturer responsible for the course annually.

Not applicable.

Not applicable.

KAY, S.: Intuitive Probability and Random Processing using MATLAB, Springer 2005, 833 pp., ISBN 0-387-24157-4 (EN)
LEVIN, B.: Teorie náhodných procesů a její aplikace v radiotechnice, SNTL Praha: 1965, 568 s. (CS)

ANDĚL, J., Statistická analýza časových řad. SNTL, Praha (CS)
GOPI, E., S.: Algorithm Collections for Digital Signal Processing Applications Using Matlab, Springer, 2007, 190 pp., ISBN 978-1-4020-6409-8 (EN)
KOBAYASHI, H. et al: Probability, random processes, and statistical analysis, Cambridge University Press, 2012, 780 pp., ISBN 978-0-521-89544-6 (EN)
STEHLÍKOVÁ, B. a kol.: Metodologie výzkumu a statistická inference. 9. vyd. Brno: Folia univ. agric. et silvic. Mendel. Brun., 2009. II. ISBN 978-80-7375-362-7. (CS)