Prerequisites
Basic concepts of linear algebra and mathematical analysis.
Objectives
The course introduces the elementary theoretical and practical basis of discrete-time and continuous time Signals and Systems. Particular emphasis is placed on the frequency representations common in signal processing applications, the continous-to-discrete time conversion, and the analysis of linear and invariant dynamical systems.
Program
1. Basic concepts of discrete-time (dt) and continous-time (ct) signals. Examples. Transformations. 2. Basic conceps of systems. Memory, causalility, invariance, linearity, stability, invertibility. 3. Linear and time-invariant (LTI) systems. Impulse response. Convolution. Properties. 4. Laplace transform (LT). Transfer function (TF). LTI systems described by differential equations, poles and zeros. Relation between the TF and properties of LTI systems. Inverse LT and unilateral LT. 5. Fourier transform (FT) of tc signals. Representation of aperiodic signals via FT. Frequency response, filtering. Relation with the Fourier Series (FS) for periodic signals. 6. Fourier transform of td signals. Spectra of td signals. LTI systems described by difference equations. 7. Sampling. Discrete-time processing of continuous-time signals. Sampling theorem. Aliasing.
Evaluation Methodology
50% continuous evaluation / 50% non-continuous evaluation
Cross-Competence Component
Working in group stimulates the development of collaboration skills, including assignment of different roles to group members, as well as oral and written communication.
Laboratorial Component
Five lab assignments (the first one will not be graded), where the students have the opportunity to experiment with real-world and synthetic signals that illustrate the concepts conveyed in the lectures. Students work in groups of three and should submit one report for each graded assignment (moodle submission).
Programming and Computing Component
Elementary programming in Matlab for signal analysis and simulation of simple dynamical systems.
More information at: https://fenix.tecnico.ulisboa.pt/cursos/lerc/disciplina-curricular/845953938490013
