# SIGNAL THEORY - channel 2

ING-INF/03 - 9 CFU - 2° Semester

LAURA GALLUCCIO

## Learning Objectives

-Being able to analyze simple problems described in a probabilistic way;

-Being able to analyze the characteristics of random signals;

-Being able to mathematically describe linear systems and how they transform random signals.

-Being able to analytically characterize the basic components of a communication system

## Detailed Course Content

Part 1. Probability Theory

Random experiment; probability, Bayes theorem; total probability theorem; Random variables, probability density function and cumulative distribution; transformation of a random variable; indexes of a distribution; Gaussian random variable, other relevant random variables (e.g. uniform random variable, Poisson random variable, Bernoulli random variable, exponential random variable), central limit theorem.

Part 2. Analysis of Periodic and Continuous Signals

Definitions and examples of signals; elementary properties of signals; Harmonic analysis of periodic signals; amplitude and phase spectra of signals and their properties; synthesis of a signal from a finite number of harmonics. Fourier integral; Fourier transform; Fourier transformtheorems (linearity, duality, delay, scale change, modulation, derivation, integration, product, convolution); Dirac delta generalized function and its transformation; Periodicization of a signal and Poisson formulas; Sampling theorem.

Part 3. Linear and stationary systems

Definition of "system" and transformation of a signal through a system; properties of one-dimensional systems; characterization and analysis of stationary linear systems (impulse response and frequency response); ; decibels; cascading and parallel systems; Ideal filters ( low pass, high pass, band pass, delete band; real filters; signal bandwidth; distortion due to the filtering process; Parseval theorem and spectral energy density; spectral power density; autocorrelation function; Wiener-Khintchine theorem.

Part 4. Elementary transformations of random signals

Random processes; parametric random processes; Stationary processes; Filtering of a stationary random process; spectral power density of a stationary random process; White noise and thermal noise; Ergodicity of a process.

## Textbook Information

1) Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill

2) Leon Couch: Fondamenti di Telecomunicazioni, VII Ed. Pearson, Prentice Hall

Open in PDF format Versione in italiano