Course detail

# Signals and Systems

FEKT-BPA-SASAcad. year: 2023/2024

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.

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

35 points for individual projects
65 points for final exam
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.

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.

Study aids

Not applicable.

Prerequisites and corequisites

• compulsory prerequisite

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

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 hours, optionally

Teacher / Lecturer

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 hours, compulsory

Teacher / Lecturer

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