Introduction to Linear Signals and Systems

Code:

EEC0013

Acronym:

TSIN

Keywords
Classification	Keyword
OFICIAL	Basic Sciences for Electrotechnology

Instance: 2018/2019 - 1S

Active?	Yes
Web Page:	https://www.fe.up.pt/si/conteudos_geral.conteudos_ver?pct_pag_id=1639&pct_parametros=p_ano_lectivo=2011/2012-y-p_cad_codigo=EEC0013-y-p_periodo=1S
Responsible unit:	Department of Electrical and Computer Engineering
Course/CS Responsible:	Master in Electrical and Computers Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEEC	328	Syllabus	2	-	6	28	28

Teaching language

Portuguese

Objectives

1. To describe and explain essential concepts, characteristics, properties and operations of signals and systems;
2. To identify and distinguish continuous/discrete signals and systems;
3. To define, explain, operate and solve time invariant linear systems, continuous and discrete, in  time and frequency (Fourier) domains.
4. To interpret and calculate Laplace and Z transforms and relate them with time invariant linear systems.
5. To decompose signals and systems and illustrate them;
6. To analyse time invariant linear systems and represent them in time and frequency.

Learning outcomes and competences

At the end of the course the student must be proficient in:

Describing and explaining the essential concepts, characteristics, properties and operations of signals and systems;

Understanding and solving  time invariant linear systems, continuous and discrete, in  time and frequency (Fourier) domains.

Calculating and understanding Laplace and Z transforms and relate them with time invariant linear systems.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Basic knowledge in mathematical analysis, algebra and circuit theory.

Program

CONTENTS
Continuous and discrete signals and systems; Time invariant linear systems; Linear convolution; Fourier analysis for signals and systems; Frequency response; Introduction to bilateral and unilateral Laplace and  Z transforms.

SYLLABUS
1. Continuous and discrete signals and systems
1.1 Basic continuous and discrete signals
1.2 Systems and their properties (with or without memory, invertibility, causality, stability, temporal invariance, linearity)
2. Time invariant linear systems
2.1 Representation of signals by impulses
2.2 Convolution integral
2.3 Systems described by differential equations and difference equations
3. Fourier analysis for signals and systems
3.1 Signals and continuous systems
3.1.1 Response of time invariant linear systems to complex exponentials
3.1.2 Representation and approximation of periodic signals (Fourier)
3.1.3 Representation of aperiodic signals by Fourier transform
3.1.4 Bilateral and unilateral Laplace transform; Definitions and region of convergence; Applications

3.2 Discrete signals and systems
3.2.1 Response of time invariant linear systems to complex exponentials
3.2.2 Representation of periodic signals by discrete Fourier series
3.2.3 Representation of aperiodic signals by discrete Fourier transform
3.2.4 Frequency response of systems of first and second order, characterized by linear difference equations with constant coefficients.
3.2.5 Bilateral and unilateral Z transform; Definitions and convergence region; Applications
4. Sampling.

Mandatory literature

Oppenheim, Alan V.; Signals & systems. ISBN: 0-13-651175-9
Michael J. Roberts; Fundamentals of Signals and Systems, McGraw-Hill International Edition, 2008. ISBN: 978-007-125937-8

Complementary Bibliography

Buck, John R.; Computer explorations in signals and systems. ISBN: 0-13-732868-0
Lindner, Douglas K; Introduction to signals and systems. ISBN: 0-07-116489-8
Signals and Systems-MIT open course ware, MIT
H. P. Hsu; Signals and Systems, Mc Graw-Hill, 1995. ISBN: ISBN 0-07-030641-9

Teaching methods and learning activities

The lectures provide the main ideas and the guiding lines of the course with the help of examples. Details are left to self study and  problem solving, in tutorial sessions.

Software

MatLab 7

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	75,00
Participação presencial	0,00
Teste	25,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	97,00
Frequência das aulas	65,00
Total:	162,00

Eligibility for exams

The students attending the course for the first time will be excluded from the final exivo anterior am, if they miss more than 25% of the problem solving tutorials.

Calculation formula of final grade

Two  components are taken into account:

- Mid term test – 1mini-tests, which will not last more than 1h 30m (AD)
- Written Exam – a final exam, which will not last more than 2h 30m (CF)
 

The final mark for these students will be calculated by the formula CF =max(0,25 AD + 0,75 EF, EF). 

Examinations or Special Assignments

Not applicable

Internship work/project

Not applicable

Classification improvement

Students approved in the regular final exam may have optional access to a special designed exam if they wish to raise their final mark. The classification obtained in this exam substitutes the previous one, if it is higher. Note that in this case the continuous assessment is discarded, and the classification is given by the exam alone.

Observations

Students may only achieve very high grades, namely 19 and 20 out of 20, if they obtain a compatible result in a special oral exam in the face of a jury composed by at least two members of the teaching staff.

Even though is it not written in the program and aims of the course, students should use the computer resources available. In FEUP’s network Matlab is available, a powerful computer tool. It can be used countless tools, simulators and the system of John Hopkins University.

Regular visits to the open course ware site are also stimulated, namely the signals and systems course home.