Course detail

Signals and Systems

FEKT-BPA-SASAcad. year: 2024/2025

This module provides an introduction to the linear time-invariant continuous- and discrete-time signals and systems. Students are introduced with the various methods of description and analysis of the continuous- and discrete-time signals and systems: time domain, frequency domain, spectrum, Fourier series, sampling, transforms (Laplace, Fourier, Z) and difference or differential equations. These methods are used to analyse signals and systems properties and to determine basic characteristics: linearity, time-invariance, causality, stability, etc. 

The subject also includes an introduction to the statistical analysis of signals with a random component. 

Language of instruction

English

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

Ing. Miroslav Jirgl, Ph.D.

Department

Department of Control and Instrumentation (UAMT)

Offered to foreign students

Of all faculties

Entry knowledge

Student should have sufficient knowledge of the mathematical analysis for bachelors, mainly: differential and integral calculus, series, basic transforms and complex numbers.

Rules for evaluation and completion of the course

30 points for individual projects
70 points for final exam
The content and forms of  instruction in the evaluated course are specified by a regulation issued by the guarantee of the course and updated for every academic year. 

Aims

To acquaint with the fundamentals of signals and systems with the continuous and discrete time. To learn to apply the fundamentals to real signals and systems.
An absolvent is able to:
- describe continuous and discrete time signals in time and frequency domain,
- perform continuous and discrete time signal transform using the Fourier series, the Fourier transform, the Laplace transform and the Z-transform,
- discuss practical interpretations of these transforms and their properties,
- describe fundamental properties of LTI continuous-time systems,
- describe fundamental properties of LTI discrete-time systems,
- use the different methods to describe LTI systems,
- determine system response of an LTI system to standard and general signals,
- determine from the description of the LTI system its characteristics such as linearity, time-invariance, causality and stability.

- define the random variable and apply appropriate mathematical and statistical methods to the basic analysis of random processes. 

Study aids

Not applicable.

Prerequisites and corequisites

Basic literature

OPENHEIM, Alan, WILSKY, Alan. Signals and Systems. Second edition. New Jersey: Prentice Hall 1997, 957 s. ISBN 0-13-814757-4. (EN)

Recommended literature

Not applicable.

Classification of course in study plans

  • Programme BPA-ELE Bachelor's

    specialization BPA-PSA , 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Jitka Poměnková, Ph.D.
Ing. Miroslav Jirgl, Ph.D.

Syllabus

1 Introduction, motivation, classification of signals.
2 Continuous-time signals - overview, definition, basic operations and manipulation. Introduction to the Fourier series.
3 Fourier series and Fourier transformation, frequency spectrum of a signal. Examples.
4 Concept of continuous-time linear system, differential equation, its solution, Laplace transform. Examples.
5 Transfer function, poles and zeros, frequency responses. Examples.
6 Step response, impulse response. System stability. Examples.
7 Introduction to discrete transformations (Discrete Fourier transform, Z transform), sampling of a continuous-time signal.
8 Concept of discrete-time linear system, basic characteristics of discrete systems.
9 Discrete filters.
10 Random variable.
11 Random processes.
12 Correlation and spectral analysis.
13 Summary and revision.

Exercise in computer lab

26 hod., compulsory

Teacher / Lecturer

Ing. Miroslav Jirgl, Ph.D.
doc. RNDr. Jitka Poměnková, Ph.D.

Syllabus

1-2 Introduction to MATLAB environment. Basic manipulations with signals.
3-4 Basics of the Fourier analysis, introduction to the continuous-time LTI systems.
5-6 Continuous-time LTI systems and their characteristics.
7-8 Modelling of a discrete-time system.
9-10 Filter designer.
11-12 Modelling of discrete filters.

E-learning texts

MANDAL, Mrinal Kr a Amir ASIF. Continuous and discrete time signals and systems [online]. Cambridge: Cambridge University Press, 2007 [cit. 2022-09-16]. ISBN 978-0521854559.
Continuous_and_Discrete_Time_Signals_and_Systems.pdf 6.04 MB