Course detail

Selected Lectures on Mathematics

FEKT-MPA-SLMAcad. year: 2024/2025

The proposed course is a compulsory basic theoretical course profiling the basis, which focuses on the use of selected mathematical methods in the field of space technology. It provides not only a theoretical apparatus for the design and implementation of space applications, but also their practical verification in simulations. The Matlab programming environment will be used for this purpose.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Jitka Dluhá, Ph.D.

Department

Department of Radio Electronics (UREL)

Entry knowledge

Mathematical subjects and knowledge , including the basics of statistics and signal processing, are required.

Rules for evaluation and completion of the course

In general:
- obtaining credit on the basis of a test for 16 points and active participation in exercises for 14 points (max. 30 points, min. 15 points),
- Written parts of the final exam (max 70 points, minimum 35 points)
The definition of the controlled education and the way of its implementation are stipulated by the updated guarantor's annual regulation.

Aims

The aim of the course is to present to students a specialized mathematical-statistical apparatus, which is important for understanding and interconnecting the principles of electrical and mechanical systems and practical verification of acquired skills.
After completing the course, students should be able to independently solve problems associated with mathematical modeling, verification and testing of designs for space applications.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

KAZ, S. Fundamentals of Statistical signal processing. Estimation Theorz. Prentice Hall, New Jersey, 2011, 595 pp. ISBN 0-13-345711-7 (EN)
MOON,T., STIRLING, W. Mathematical Methods and Algorithms for Signal Processing, Prentice Hall, New Jersey 2000, pp. 978. ISBN 0-201 -361 86-8 (EN)

Recommended reading

JAN, J. Číslicová filtrace, analýza a restaurace signálů. vědecké monografie. vědecké monografie. Brno: VUTIUM Brno, 2002. 427 s. ISBN: 80-214-1558- 4.
JAN, J. Digital Signal Filtering, Analysis and Restoration. volume 44. volume 44. London: The Institution of Electrical Engineers, 2000. 407 s. ISBN: 0-85296-760- 8.
REKTORYS, K. Přehled užité matematiky I, II, Prometheus, Praha 2002, 720 s., ISBN80-7196-181-7 (EN)

Classification of course in study plans

  • Programme MPA-SAP Master's 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Jitka Dluhá, Ph.D.

Syllabus

1. Course introduction. 2. Selected linear transform (Self-study) 3.  Impulse characteristic and transfer functions. 4. Filtering and filters. 5. Random variable. Random Vectors. 6. Reliability of systems. 7. Random processes. 8. Correlation and Spectral analysis. 9. Estimation: Theory and Applications 10. Detectors and Detection 11. Criterion and Parameter Estimation. 12.-13. Individual Project Presentation.

 

 

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Jitka Dluhá, Ph.D.

Syllabus

1. Exerciser’s introduction. 2. Assignment of Individual Work 1,2 and Individual Project 3. Modelling of a system. 4. Modelling of a filter. 5. Filters and filtering (Self-study). 6. Modelling of a random variable. 7. Reliability of systems. 8. Random process analysis. 9. Estimation and testing in Matlab. 10. Testing of GWN. 11. Detection of signals hidden in noise. 12.-13. Individual Project Presentation.