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Signals and Systems

Code: FIS2012     Acronym: FIS2012

Classification Keyword

Instance: 2018/2019 - 2S

Active? Yes
Responsible unit: Department of Physics and Astronomy
Course/CS Responsible: Master's Degree in Physical Engineering

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
MI:EF 64 study plan from 2017/18 2 - 6 56 162

Teaching Staff - Responsibilities

Teacher Responsibility
José Manuel Monteiro Moreira

Teaching - Hours

Theoretical classes: 2,50
Theoretical and practical : 1,50
Type Teacher Classes Hour
Theoretical classes Totals 1 2,50
José Manuel Monteiro Moreira 2,50
Maria de Fátima Gonçalves da Mota 0,00
Theoretical and practical Totals 2 3,00
José Manuel Monteiro Moreira 3,00

Teaching language

Português - Suitable for English-speaking students


To know the methodologies and physical / mathematical techniques for the study of signals and important systems in physics and engineering. • Understand the central characteristics of linear and time invariant systems (LTI). • Master the behavior of LTI systems actuated by continuous or discrete signals, including the actual situation where signals are degraded by the presence of noise. • Understand the principles of system control and the techniques used in its study. • Understand the vast domain of application of the principles, methodologies and techniques studied.

We intend to give a clear and modern view of the techniques used in the study of signals and systems. In particular we study the Fourier series, Fourier integrals, FFT and Laplace transforms of continuous and discrete time signals. The concept of transfer function is fundamental and studied in detail as well as the impulse response. Communication systems are also studied.

Learning outcomes and competences

The student will have finished the course the possibility of studying and characterizing with detail continuous and discrete signals and given a linear system and invariant in time know his answer.

Working method


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

Complex analysis.
Differential equations and finite differences.


1. Signals and systems. Continuous and discrete signals. Energy and power. Exponential and sinosoidal signals. Period. The unit impulse and the step of Heaviside. Distributions and their properties. Associations of systems and basic properties. Linear and invariant systems in time LTI).
2. LTI systems. The convolution sum. The convolution integral. Properties. Application examples. Cause and stability.
3. The Fourier series representation of periodic functions.
4.The Fourier transform of continuous functions of time.Properties.Applications.Resolution of differential equations using the Fourier transform.
5. The Fourier transform of discrete time functions, periodic or not.Properties and applications.Resolution of equations to finite differences using this transform.
6. Characterization of signals and systems in time and frequency. Bode diagrams and their applications.
7.Translations of Laplace.Properties and their applications.

Mandatory literature

Oppenheim Alan V.; Signals and systems. ISBN: 0-13-811175-8
Girod Bernd; Signals and systems. ISBN: 0-471-98800-6

Teaching methods and learning activities

The usual methodology will be followed. Theoretical and theoretical-practical classes given in the framework or rectro projected.
Type of Assessment: Assessment by 2 frequencies or final exam.

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation Weight (%)
Exame 45,00
Participação presencial 10,00
Teste 45,00
Total: 100,00

Amount of time allocated to each course unit

designation Time (hours)
Estudo autónomo 100,00
Total: 100,00

Eligibility for exams

Conditions for access to assessement: The FCUP regulations will be followed.

Calculation formula of final grade

Assessment formula: The average grade of the tests provides exemption from examination if it is equal to or greater than 9.5 values. If the student in these conditions is for examination the valid note will be the major of the two.

Classification improvement

The average grade of the tests gives exemption of exam if it is equal or superior to 9.5 values. If the student in these conditions is for examination the valid note will be the major of the two.
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