English

4

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: (1) quantifying the probability of the event, (2) distinguishing between the random variables and describe their characteristics, (3) to test the hypothesis by parametric and non-parametric way, (4) describe the probability density by Gaussian mixture models, (5) estimating the shape of the spectrum and identify the spectral components, (6) identify and test the presence of a signal in noise.

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. Techning methods include lectures, computer laboratories.

Requirements for completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every. Test written during semester (30 points), final oral+ writting test exam (70 points).

Lectures:
1. Calculations on the discrete and the continuous distribution of random variables. Simulation in Matlab.
2. The simulation of the distribution of the data set and its estimation in Matlab.
3. Calculation of confidence intervals, the derivation of system reliability.
4. Testing the significance of the estimates, the parametric and the nonparametric approach.
5. Examples of Gaussian mixed models.
6. Calculation and testing for the presence of signal in the channel, goodness of fit tests.
7. Spectrum estimation techniques (parametric and nonparametric methods).
8. Gaussian mixed models.
9. Random processes.
10. Spectrum estimation techniques (parametric and nonparametric methods).
11. Detection of hidden signals in noises. ROC curve.
12. Applications - time-frequency analysis.
13. 10. Orthogonal transformation, Karhunen-Loev transformation, PCA.

Computer exercises:
1. Calculations on the discrete and the continuous distribution of random variables. Simulation in Matlab.
2. The simulation of the distribution of the data set and its estimation in Matlab.
3. Calculation of confidence intervals, the derivation of system reliability.
4. Testing the significance of the estimates, the parametric and the nonparametric approach.
5. Examples of Gaussian mixed models.
6. Calculation and testing for the presence of signal in the channel, goodness of fit tests.
7. Application of estimation methods on simulated signal spectrum.

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.

KOBAYASHI, H. et al. Probability, random processes, and statistical analysis, Cambridge University Press, 2012. (EN)

GOPI, E.S. Algorithm Collections for Digital Signal Processing Applications Using Matlab, Springer, 2007. (EN)
KAY, S. Intuitive Probability and Random Processing using MATLAB, Springer 2005. (EN)

13 hours, compulsory

1. Calculations on the discrete and the continuous distribution of random variables. Simulation in Matlab. The simulation of the distribution of the data set and its estimation in Matlab.
2. Calculation of confidence intervals, the derivation of system reliability. Testing the significance of the estimates, the parametric and the nonparametric approach.
3. Examples of Gaussian mixed models.
4. Examples of orthogonal transformation.
5. Calculation and testing for the presence of signal in the channel, goodness of fit tests.
6. Application of estimation methods on simulated signal spectrum.