Systems and Signals

Objectives

The course introduces the elementary theoretical and practical basis of discrete-time and continuous time Signals and Systems. Particular emphasis is 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. Exemples. Transformations.
2. Basic conceps of systems. Memory, causalility, invariance, linearity, stability, invertibility.
3. Linear and time-invariant (LTI) systems. Impulse response. Convolution. Properties.
4. Fourier series (FS) of tc signals. Exponentials as proper functions of LTI systems. Representation of periodic signals by the FS.
5. Fourier transform (FT) of tc signals. Representation of aperiodic signals via FT. Frequency response, filtering.
6. Fourier transform of td signals. Concept of spectrum of td signal. LTI systems described by difference equations.
7. Sampling. Discrete-time procssing of continuous-time signals. Sampling theorem. Aliasing.
8. Laplace transform (TL). Transfer function (TF). LTI systems described by differential equations, poles and zeros. Block diagram sand equivalent TFs. Unilateral TL.
9. Bode plots.

Teaching Methodologies

50% continuous evaluation / 50% non-continuous evaluation

Bibliography

"Signals and Systems", Alan V. Oppenheim e Alan S. Willsky, Prentice-Hall, 2ª edição, 1996.