Course detail

Signal Detection and Estimation Theory

FEKT-MPA-SDEAcad. year: 2023/2024

The compulsory elective course "Signal detection and estimation theory" is focused primarily on the detection of signals and estimation of their parameters. In the first part of the course, students will be familiarized with the mathematical and statistical apparatus needed for the above areas. Selected areas of linear algebra and the theory of random processes will be discussed. The second part is devoted to statistical decision theory, parameter estimation and detection, and also the basic theory of reliability is mentioned. The third part contains general information about LTI systems, filtering, Kalman filtering and Hilbert transforms.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Entry knowledge

It is required knowledge of the related mathematical basis, including the statistics and signal processing fundamentals.

 

Rules for evaluation and completion of the course

The conditions for successful completion of the course are given in the annually updated decree of the course guarantor. Students will be evaluated by credit on the basis of gaining points from practice (max. 30 points, min. 15 points) and the final exam (max. 70 points, min. 35 points). Exercise points can be obtained by test in exercises (max. 15 points) and individual work (max. 15 points). The test consists of numerical or graphical examples and analysis of the data sets in MATLAB. The test cannot be repeated. Absence from the exam for serious reasons will be solved individually. The final exam can be obtained on the basis of written (max. 60 points) and oral (max. 10 points) part. The written final exam consists of two parts, a numerical part and a theoretical part, and covers the content of lectures and exercises.
The definition of controlled teaching and the method of its implementation is determined by the annually updated decree of the subject guarantor. Computer exercises are mandatory.

Aims

The aim of the course is to familiarize students with selected topics of mathematics, statistics and signal processing, which are needed for successive specialized courses. The course includes selected operations of linear algebra and matrix decomposition, theory of random variables and random processes, introduction to system reliability, detectors and signal detection, parameter estimation, Kalman filtering and Hilbert transform.

The graduate of the course is able to: (a) apply mathematical techniques related to selected areas of the field of study, (b) apply decision and detection theory, (c) estimate signal parameters and examine an estimation quality, (d) use general and Kalman filtering techniques in relevant areas signal processing, (e) apply the Hilbert transform to determine complex functions. 

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

BARKAT, M. Signal Detection and Estimation. 2nd ed. Norwood: Artech House, 2005. ISBN: 9781580530705 (EN)
MOON, T. K., STIRLING, W. C. Mathematical Methods and Algorithms for Signal Processing. New Jersey: Prentice Hall, 2000, ISBN: ‎978-0201361865 (EN)

Recommended reading

HIPPENSTIEL, R. D. Detection Theory: Applications and Digital Signal Processing, 1st edition,CRC Press, 2001, ISBN: 9780849304347 (EN)

Classification of course in study plans

  • Programme MPA-AEE Master's 1 year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Syllabus

1. Course introduction.

2. Decomposition methods

3. Signal processing – statistical approach

  • Random Variables
  • Random Vectors
  • Random Processes (I+II)
  • Reliability of systems

4. Signal detection and estimation theory

4.1 Statistical Decision Theory.

4.2 Parameter Estimation I and II

4.3 Filtering.

4.4 Detection theory

4.5 Detectors and its evaluation

5. Hilbert transform

 

Exercise in computer lab

26 hod., compulsory

Teacher / Lecturer

Syllabus

1. Course introduction.

2. Decomposition methods

3. Signal processing – statistical approach

  • Random Variables
  • Random Vectors
  • Random Processes (I+II)
  • Reliability of systems

4. Signal detection and estimation theory

4.1 Statistical Decision Theory.

4.2 Parameter Estimation I and II

4.3 Filtering.

4.4 Detection theory

4.5 Detectors and its evaluation

5. Hilbert transform