Course detail

# Signals and Systems

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.

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.

• compulsory prerequisite

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Chi-Tsong Chen:System and Signal Analysis,Saunders College publishing, 1994. (EN)
OPENHEIM, Alan, WILSKY, Alan. Signals and Systems. Second edition. New Jersey: Prentice Hall 1997, 957 s. ISBN 0-13-814757-4. (EN)
CHI-TSONG CHEN. System and Signal Analysis. Oxford University press 2004. 424 s. ISBN 0-19-515661-7. (EN)

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

30 points for individual projects
70 points for final exam

Language of instruction

English

Work placements

Not applicable.

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.

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.

Classification of course in study plans

• Programme BPA-ELE Bachelor's

specialization BPA-PSA , 2. year of study, winter semester, 6 credits, compulsory

#### Type of course unit

Lecture

52 hours, optionally

Teacher / Lecturer

Exercise in computer lab

13 hours, compulsory

Teacher / Lecturer