Subject: Signals and Systems

Scientific Area:



80 Hours

Number of ECTS:

7,5 ECTS



Overall objectives:

1 - Understanding the concepts related to mathematical manipulation of signals and systems. Apply the relation between signals and vectors to the development of the main operations between signals and tranforms. Apply the Fourier transform, for the continuous and discrete domain, Laplace transform and Z transform to the analysis of signals and systems. In practical need to sample a continuous signal, understand the implications resulting from the sampling of signals. In the context of system analysis are the provided the fundamentals of control theory.
2 - Introduce the software Matlab, by carrying out small pratical works that focus on the material taught.


1 - Fundamental Concepts: characterization and classification of signal; most important signals; graphical analysis of signals; definitions of systems.
2 - Signals and vectors: identification signal-vector; vector space of functions; scalar product; operations on signals; correlation coefficient; correlation function.
3 - Convolution: definition; convolution versus correlation; convolution expressions; properties.
4 - Fourier series: general process of decomposition of signals; exponential Fourier series; trigonometric Fourier series; symmetries of signals; Parseval's theorem.
5 - Fourier transform: direct and inverse transform; properties; Fourier transform for n dimensions; limits of spectrum; Fourier transform of discrete signals; sampling theorem; DFT; Fast Fourier Transform (FFT).
6 - Laplace transform: generalized concept of frequency; directan and inverse transform; convergence region; properties; the inversion of Laplace transform; initial and final value theorems; analysis of systems using the Laplace transform; solving differential equations with initial conditions.
7 - Z-transform: direct and inverse transforms; region of convergence; properties; calculation of the inverse transform; initial and final value theorems; analysis of systems using the Z transform; solving difference equations with initial conditions.
8 - Filters


Azevedo, J. A. R , 2010 , Apontamentos de Sinais e Sistemas , Universidade da Madeira
F. C. Velez Grilo, António, M. E. S. Casimiro, J. A. C. Lopes e J. A. R. Azevedo , 2010 , Teoria do Sinal e suas aplicações , Escolar Editora
J. L. Martins de Carvalho , 1993 , Dynamical Systems and Automatic Control , Prentice Hall International

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Oral examinations: Oral evaluations aim to develop oral communication skills and also enables assessment of the taught knowledges. The student is confronted with some issues that should respond by demonstrating knowledge and revealing critical thinking. Note that the student is advised to keep a plan of continued study and work throughout the semester.

Practical and laboratory work: Practical work is assessed by reports, presentations or discussions. This allows students to develop skills of design, writing, presentation of results, developing of oral communication skills and teamwork.

Projects: Project work allows students to develop research work, which can include reading papers of the specialty. Students must prepare a report and make a presentation as a seminar.

Tests: They can be mini-tests or exam. The mini-tests have the objective to evaluate theoretical knowledges and problem solving. Thus, the students may evaluate their performance and change strategies if necessary. The assessment ends with a final exam that covers the various topics of the curricular unit. Beyond the objectives of evaluation, the importance of this examination focuses on students' ability to relate different topics.