SIGNALS AND SYSTEMS
Learning outcomes of the course unit
The aim of this course is to introduce the students to Analog Signalsand to the transformations that they undergo when processed by (Analog)Linear Systems. Signals and Systems constitute the basic buildingblocks for the analysis and design of telecommunication systems and,more generally, of electronic systems for information processing. Tothis aim, most of the course is dedicated to studying the methods forrepresenting signals and systems "in the frequency domain", which is anengineering tool of primary importance.
For this course, it is assumed that the student already hasagoodknowledge of Probability Theory and Random Variables. Suchtopicsarecovered, at Parma University, in the course Teoria deiSegnali A
Course contents summary
SIGNALS AND SYSTEMS IN THE TIME DOMAIN
Classification of signals. Periodic and symmetric signals. Someremarkable signals. Duration, area, mean value, energy and power of asignal. Elementary transformations on signals. The Dirac delta pulse.
Classification of systems. Linear and stationary systems. Theimpulse response. Properties of convolution: cascaded and parallelsystems. Graphical method for convolution. System properties expressedthrough the impulse response. Identification in frequency: the transferfunction.
SIGNALS AND SYSTEMS IN THE FREQUENCY DOMAIN
The Fourier series. The Fourier transform. Mathematical issuesregarding the Fourier transform. Filtering of impulsive signals.Amplitude, phase and energy spectra: the Rayleigh theorem. Symmetriesin the Fourier transform. Basic properties of the Fourier transform:linearity, change of scale, time shift. Frequency shift property(complex modulation). Review of amplitude modulation (AM).Differentiation and integration properties. Systems defined byintegral-differential equations. Review of frequency modulation (FM).Differentiation in the frequency domain. Other properties: convolutionand product. Analysis of block diagrams in the frequency domain. Finalproperties: conjugation and correlation. Wiener-Kintchine theorem fordeterministic signals.
Transform of a Dirac pulse and of a constant. Non distortingchannel, linear distortions and equalization. Transform of a phasor anda sinusoid. Transform of the unit step. The Dirac impulse train.Spectrum of periodic signals. Filtering of periodic signals. Powerspectral density of periodic signals: the Parseval theorem. Thesampling theorem. Non ideal sampling.
Examples of stochastic processes. Statistics of a process. Markovand Gaussian processes. Expectations of a process: statistical mean andpower, autocorrelation, autocovariance. Stationarity. Properties of theautocorrelation for WSS processes. Ergodicity. Ergodicity with respectto the mean value and to the autocorrelation. Filtering of randomsignals: the power spectral density. White noise. Amplitude modulationand sampling of a random signal.
A. Vannucci, "Segnali Analogici e Sistemi Lineari: un corso di Teoriadei Segnali per le lauree triennali in ingegneria", Pitagora Editrice,Bologna, 2003.
Two written tests are held during the semester. In case of anegativeevaluation, the student is required to pass a written testfollowed byan oral exam.