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Introduction to Linear Signals and Systems

Code: EEC0013     Acronym: TSIN

Classification Keyword
OFICIAL Fundamental and Electrotechnics Sciences

Instance: 2011/2012 - 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 435 Syllabus (Transition) since 2010/2011 2 - 6 63 162
Syllabus 2 - 6 63 162

Teaching language



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 invariant linear systems, continuous and discrete, in the domains of time and frequencies (Fourier).
4. To interpret and calculate Laplace and Z transforms and relate them with invariant linear systems.
5. To decompose signals and systems and illustrate them;
6. To analyse invariant linear systems and represent them in time and frequency.


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

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. Invariant linear systems
2.1 Representation of signals by impulses
2.2 Invariant linear systems; 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 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 Frequency response to system of first and second order, which are characterized by linear differential equations with constant coefficients.
3.1.5 Bilateral and unilateral Laplace transform; Definitions and region of convergence; Applications
3.2 Discrete signals and systems
3.2.1 Response of 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 Response in frequency systems of first and second order, which are characterized by linear differential 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

Teaching methods and learning activities

Standard methods are used in teaching Signal Theory. Lectures are given with some but intentionally limited graphical display support. Exercises in practical classes are dominantly a student-centered activity, namely by means of discussing the homework problems assigned. Students are also encouraged to use MatLab tools for out-of-class self-study.


MatLab 7

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description Type Time (hours) Weight (%) End date
Attendance (estimated) Participação presencial 50,00
Midterm Exame 3,00 2011-11-09
Final exam Exame 3,00 2012-02-10
Study for final exam Exame 25,00 2012-02-10
Total: - 0,00

Amount of time allocated to each course unit

Description Type Time (hours) End date
Study along semester Estudo autónomo 75 2011-12-16
Total: 75,00

Eligibility for exams

A student is given access to the final exam if he or she achieves a minimum score of 30% in continuous assessment. The score is given by the teaching staff of the practical classes, based on the performance of the students and on their commitment. The performance evaluation is dominated by the results achieved in a large number of so called micro-tests (6 to 8 in the semester, answered in 10 minutes at the end of some practical classes).

Calculation formula of final grade

Two different components are taken into account:

- Continuous Assessment – a mini-test, which will not last more than 1h 30m
- Written Exam – a final exam, which will not last more than 2h 30m

In order to assess aims 1, 2, 3 and 4 specific questions will be asked in both components of assessment, which may be multiple choice questions.
In order to aims 3, 4, 5 and 6 be assessed, students will have to do solve problems similar to those done in classes.

Note: Students cannot use calculating machines or mobile phones during the mini-test and the final exam. Students will get a form.

The mark of ordinary students will be based on the average mark of the mini-test (20%) and final exam (80%).

This average of both components will only be taken into account in normal and recurso season. If students want to improve their marks, the only component which will be taken into account is the final exam.

Students who do no attend to the mini-test will earn a 0. However, if their absence is adequately justified, they can attend to the final exam, which will worth 100% of the final mark.

Examinations or Special Assignments

As mentioned above the students are required to answer short duration micro-tests, proposed at the end of roughly half the number of practical classes. These tests address similar problems to some previously assigned homework problems. For N tests made, the average result of the best N-2 tests is the basis for the CA score, however corrected by the other objective and subjective information that the teacher has gathered for each student.

Special assessment (TE, DA, ...)

A special assessment is granted for students who are not required to attend the practical classes (e.g. working students). The final exam is made different of the one for regular students, and 30 minutes longer. The main objective of this special exam is to cover most of the subjects taught, to cater for the lack of information obtained throughout the semester.

Classification improvement

Students approved in the regular final exam have optional access to a special designed exam. 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.


Students who have got a continuous assessment (CA) score obtained in the previous teaching semester have to decide whether they want to keep it, in which case they do not answer micro-tests, or if they want to get a fresh CA, in which case the previous CA is eliminated and unrecoverable.

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


Jorge Martins de Carvalho (building I, room I-315)
Fridays: 10h00 – 11h30

Armando Jorge Padilha (building I, room I-309)
Tuesdays: 10h00 – 12h00; 15h30 – 16h30

Luís Corte-Real (building I, room I-332)
Tuesdays: 11h00 – 12h30

Paulo Lopes dos Santos (building I, room I-209)
Mondays: 11h00 – 12h00; Tuesdays: 11h00 – 13h00
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