Description

Theory
2

Laboratory
3

Instructors

Isabel Martins

Contents

1. Continuous-time (CT) and discrete-time (DT) signals. Transformations. Elementary signals.
2. CT and DT systems. Properties: memory, causality, stability, invertibility, invariance, linearity.
3. Linear and time-invariant (LTI) systems in CT and DT. Impulse response. Convolution. Properties. LTI systems described by differential equations and difference equations.
4. Laplace Transform (LT). Region of convergence (ROC). Properties. Inverse LT. Unilateral LT. Transfer function of CT LTI systems.
5. CT Fourier Series (FS). Representation of periodic signals by the FS.
6. CT Fourier Transform (FT). Properties. Inverse FT. Frequency response of CT LTI systems.
7. Ideal sampling and reconstruction. Sampling theorem. Effect of subsampling (aliasing).

Learning Outcomes

This course unit aims at providing the student the knowledge of analytical tools and techniques necessary for the design and analysis of continuous-time and discrete-time linear systems, useful in several areas of engineering, namely:
-understand that the concepts of signals and systems have applications in various disciplines;
-classify and characterize signals/systems and understand the difference between continuous-time and discrete-time signals/systems;
-analyze linear and time-invariant systems (LTI) (temporal and Fourier analysis, Laplace methods);
-determine the impulse response of a LTI system from the differential equation/difference equation;
-determine the response of a LTI system to an input signal, in the time domain or through transformation to the frequency domain or the complex domain;
-understand definitions/properties of the Fourier series and the Fourier and Laplace transforms;
-calculate transforms and inverse transforms;
-understand and apply the sampling theorem;
-use professional simulation tools (MATLAB).