20810334 - SIGNAL THEORY

The course aims to provide the mathematical tools and methodologies necessary for the characterization and analysis of both deterministic and random signals used in order to send and / or store information.
At the end of the course the student will have acquired the necessary skills for the representation of signals in the time and frequency domain as well as basic notions of probability theory, random variables and random processes.
teacher profile | teaching materials


Generality on communication systems. Message and signal definition. Signal representations. The signals as elements of a vectorial space. Generalized Fourier Representation. Cross and auto-correlation function: definition and properties. Linear transformations. Linear and time-invariant systems. I/O relations: convolution integral and its properties. Fourier series expansion. Fourier Transform. Parseval and Wiener theorems. Energy and power spectral density. Limited bandwidth signals. Sampling theorem. Sub-sampling effects. Hilbert transform. Analytical signal, complex envelope and low-frequency components of a band-pass signal. Bandwidth limited signals linear transformations and their samples relations.Analogic signals amplitude modulation.

Axiomatic theory of probability. The axioms of probability. Bayes' theorem. Random variables. Distribution and probability density function. Mean, variance, moments, covariance matrix. Characteristic function. Functions of one random variable. Multiple random variables: joint distributions. Conditional distributions. Central limit theorem. Gaussian random variables: univariate and multivariate. Bernoulli random variable. Poisson random variable. Laws of large numbers. Stochastic processes: general concepts. Stationary processes. Ergodic processes and related theorems. Parametric stochastic processes. Linear and non-linear transformation of stochastic ergodic processes. Continuous-time random processes; gaussian process, P.A.M. random process, armonic process.

Core Documentation

Roberto Cusani- Teoria dei Segnali - Edizioni Efesto
Probability, Random Variables, and Stochastic Processes, Athanasios Papoulis, S. Unnikrishna Pillai, McGraw-Hill 2002

Reference Bibliography

Gaetano Scarano, Segnali, Processi Aleatori, Stima, Sapienza Università Editrice, 2009

Type of delivery of the course

The course is held face-to-face


Attendance is not mandatory but recommended

Type of evaluation

During the course there will be ongoing tests aimed at assessing the students' preparation. There will be two written tests: a) the first aimed at assessing the student's ability to analyze b) the second aimed at evaluating the theoretical knowledge of the student.