Course detail

Signals and Systems

FEKT-BPA-SASAcad. year: 2022/2023

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.

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

Learning outcomes of the course unit

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.

Prerequisites

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

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods include lectures with demonstrations of practical computations, and pc labs. Students have to finish individual projects during semester.

Assesment methods and criteria linked to learning outcomes

35 points for individual projects
65 points for final exam

Course curriculum

1. General introduction and motivation; continuous and discrete world, signals classification.
2. Continuous-time and discrete-time signals - basic operations and manipulations, discretization of continuous-time signals.
3. Frequency domain of the continuous-time signal, the Fourier series.
4. The Fourier transform, examples.
5. Time and frequency domain of the discrete-time signal, the discrete Fourier series, the discrete Fourier transform (DFT).
6. Systems – definition, classification, the examples of real systems.
7. Continuous-time LTI system – description using the differential equations, the Laplace transform.
8. Continuous-time LTI system – transfer function, poles and zeros, stability of LTI systems.
9. Continuous-time LTI system – response on the standard input signals, the relation to the BIBO stability.
10. Discrete-time LTI system - description using the difference equations, the Z-transform.
11. Discrete-time LTI system – transfer function, poles and zeros, stability of LTI systems.
12. Discrete-time LTI system – response on the standard input signals, the relation to the BIBO stability.
13. Summary.

Work placements

Not applicable.

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.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Recommended optional programme components

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 reading

Not applicable.

Elearning

eLearning: currently opened course

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

52 hod., optionally

Teacher / Lecturer

Ing. Miroslav Jirgl, Ph.D.

Syllabus

Introduction, motivation, continuous-time signals.
Fourier transform, fequency spectrum. Examples.
Linear, continuous-time systems, differential equation, Laplace transform. Examples.
Transfer function, zeros and poles, frequency response. Examples.
Frequency characteristics of the linear system. Examples.
Step response, impulse response. Examples.
Stability of the continuous-time systems. Examples.
Discrete-time signals, sampling of the continuous-time signal. Examples.
Discete Fourier transform, the spectrum of the discrete-time signal. Examples.
Discrete-time system, difference equation, Z transform. Examples.
Transfer function, zeros and poles, frequency response, fequency characteristics. Examples.
Step response, impulse response, stability of the discrete-time systems. Examples.
Discretization of continuous-time systems. Examples.

Exercise in computer lab

13 hod., compulsory

Teacher / Lecturer

Ing. Miroslav Jirgl, Ph.D.

Syllabus

Basic manipulations with vectors and matrixes.
Fourier transform, amplitude and phase spectrum.
Modeling of continuous-time linear systems.
Poles and zeros, frequency respons.
Frequency charakteristic of linear continuous-time system.
Step response, impulse response of linear continuous-time system.
Stability of linear continuous-time system.
Discrete-time signals, sampling.
Discrete Fourier transform, spectrum of discrete-time signal.
Modeling of discrete-time linear systems.
Frequency response, frequency charakteristic of discrete-time system.
Step response, impulse response of discrete-time system. Stability of discrete-time system.
Discretization of continous-time systems.

Elearning

eLearning: currently opened course