Course detail

Signals and Systems

FEKT-BPC-SASAcad. year: 2022/2023

Introduction, motivation, types of signals. Continuous-time signals, Fourier transform, spectrum. Linear continuous-time systems, input-output description. Stability. Discrete time-signals, sampling. Discrete Fourier transform, spectrum. Linear discrete-time systems, input-output description. Stability of the discrete-time systems. Discretization of continuous-time systems.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

Ing. Miroslav Jirgl, Ph.D.

Department

Department of Control and Instrumentation (UAMT)

Learning outcomes of the course unit

An absolvent is able to:
- compute a freguency spectrum of continuos periodic and non- periodic signal
- demonstrate an input-output description of linear continuos system
- decide about stability of linear continuous system
- compute a freguency spectrum of discrete periodic and non- periodic signal
- demonstrate an input-output description of linear discrete system
- decide about stability of linear discrete system
- convert continuous system on discrete system

Prerequisites

Differential and integral calculus one variable, Fourier series, Fourier transform, linear differential equations, Laplace transform, linear difference equation, Z transform.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods include lectures with demonstrations of practical computations, and computer labs. Students have to write 3 tests during the semester and draw up 1 individual project.

Assesment methods and criteria linked to learning outcomes

20 points for 3 small tests / projects during semestr
15 points for individual project
65 points for final exam

Course curriculum

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

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

JURA, Pavel. Signály a systémy. Elektronické skriptum (část I, II, III), třetí opravené vydání, Brno 2016. (CS)

Recommended reading

Not applicable.

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme BPC-AMT Bachelor's 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.
Ing. Ondrej Mihálik

Syllabus

1. Introduction to MATLAB, basic operations with vectors and matrixes, 2D graphs.
2. Continuous-time signals - basic operations and manipulations with signals. Fuctions, strings and .mat files processing.
3. Continuous-time LTI systems - definition, description and properties.
4. Discrete-time signals - DFT (FFT). Loops, conditions and timing.
5. Discrete-time LTI systems - definition, description and properties. The difference equation as an algorithm.
6. Discretization of continuous-time systems. Influence of the sampling period on dynamic properties of systems. Work on project.

Elearning

eLearning: currently opened course