Class Signals and Systems

The main objective of the Signals and Systems course is to provide the students with the basics on the mathematical theory of signals and systems, sucha as: Concepts and properties of signals and systems, Linear time-invariant systems (LTI), Laplace transform, Fourier transform, Z transform, Discrete Fourier Transform, time-domain analysis, frequency-domain analysis and system transfer function. A parallel objective is to introduce the students to Matlab, which is the main tool for the laboratories. This course is a fundamental building block for more advanced subjects such as Telecommunictions, Computer Vision, Image Processing and System modeling.

1. Introduction and mathematical foundations. Imaginary numbers. Complex numbers. Operations with complex numbers. Sine and cosine. Euler equation. Inverse functions of sine, cosine and tangent. Exponential and logarithm. Derivatives and integrals.
2. Signals. Continuous and discrete signals. Properties of signals. Periodic signals, even and odd signals.
3. Singular signals.
4. Systems. Modeling systems. Linear invariant time signals. Convolution.
5. Laplace Transform. Initial value theorem. Inverse Laplace Transform.
6. Z Transform. Initial and final value theorem. Inverse Z Transform.
7. Fourier Transform. Fourier Transform of periodic signals. Fourier Transform of continuous and discrete signals.

Use of the questioning method, which aims to make questions to the students. These questions aim to understand the advantages and limitations of the subject of study.

• SINAIS E SISTEMAS (2aEd), Isabel Lourtie, Escolar Editora, 2007.
• ANÁLISE DE SISTEMAS LINEARES, Maria Isabel Ribeiro, IST Press, 2002.
• SIGNALS AND SYSTEMS, Alan V. Oppenheim e Alan S. Willsky, Prentice-Hall, 1997.
• DISCRETE-TIME SIGNAL PROCESSING, Alan V. Oppenheim e Ronald W. Schafer, Prentice-Hall, 1989.
• SIGNALS and SYSTEMS, Simom Haykin, Barry Van Veen, Wiley, 2002.
• SIGNALS and SYSTEMS. Analysis Using Transform Methods and Matlab, M. J. Roberts, McGraw Hill, 2003