## OVERVIEW

The aim of this class is to provide basic principles of spectral analysis of continuous-time signals and of their transformation through linear and nonlinear systems, of the probability theory, random variables, random processes, and of signal transmission through noisy channels.

Such topics are fundamental in relation to methods and applications that make use of signals, for both processing and analysis. Finally, background knowledge about learning and application of statistical methods is given.

## AIMS AND CONTENT

LEARNING OUTCOMES

Basic principles of signals and linear systems. Spectral analysis of continuous signals; discrete signals; sampling and analogic to digital conversion.

Random phenomena theory: probability, random variables, random processes. PAM, PCM, and analog modulations. Transmission techniques on noisy channels.

AIMS AND LEARNING OUTCOMES

In the first semester, the course aims to provide students with the basics of the theory of continuous-time signals and systems with special focus on Fourier transforms, frequency-domain analysis, and linear time invariant (LTI) systems.

Sampling is introduced both ideally and in its real versions, along with quantization and analog-to-digital conversion through the pulse code modulation (PCM) technique. Digital transmission is dealt with through wideband pulse amplitude modulation (PAM). Time-division and frequency-division multiplexing are discussed.

The theory of random phenomena is presented in the second semester, which is composed of the three parts of probability, random variables and random processes. The problem of the band-pass transmission on noisy channels is therefore addressed, describing linear modulations, AM, DSB and SSB, and angular modulations, FM and PM.

At the end of the course the student will:

- have learned the theoretical bases of continuous-time signal processing;

- have learned and know how to use the continuous-time Fourier transform;

- know how to transform periodic and aperiodic signals based on their graphical representations across the time and frequency domains;

- know under which conditions sampling allows for signal reconstruction;

- have learned and be able to use the LTI system description to address signal processing problems;

- know and be able to use the theory of wideband PAM;

- know and be able to use the theory of random phenomena;

- have learned and know how to use the theory of analog band-pass transmissions.

SYLLABUS/CONTENT

Signals and systems: Fourier series and transform, power spectral density and energy spectral density, LTI systems, filters

Sampling, quantization, and pulse code modulation (PCM)

Wideband pulse amplitude modulation (PAM)

Time division multiplexing (TDM) and frequency division multiplexing (FDM)

Probability theory

Random variables

Stochastic processes

Noise and analog modulations

PAM on noisy channels

RECOMMENDED READING/BIBLIOGRAPHY

Slides and lecture notes written by the teachers are made available to the students through AulaWeb.

A. B. Carlson, P. Crilly, Communication systems, McGraw-Hill, 2009 (5th edition).

Further reading:

M. Vetterli, J. Kovacevic, V. K. Goyal, Foundations of signal processing, Cambridge University Press, 2014.

L. Calandrino, M. Chiani, Lezioni di comunicazioni elettriche, Pitagora, 2013.

G. Gelli, F. Verde, Segnali e sistemi, Liguori, 2014.

L. Lo Presti, F. Neri, L’analisi dei segnali, CLUT, 1992.

E. M. Stein, R. Shakarchi, Fourier analysis: an introduction, Princeton University Press, 2003.

G. B. Folland, Fourier analysis and its applications, AMS, 1992.

L. Grafakos, Classical Fourier analysis, Springer, 2008.

## TEACHERS AND EXAM BOARD

**Office hours:** By appointment

Exam Board

ALDO GRATTAROLA (President)

SILVANA DELLEPIANE

LUCA MAGGIOLO

SEBASTIANO SERPICO

ANDREA TRUCCO

SANDRO ZAPPATORE

GABRIELE MOSER (President Substitute)

## LESSONS

LESSONS START

Class schedule

## EXAMS

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

13/01/2022 | 09:00 | GENOVA | Compitino | Tenendo conto dell'attuale situazione sanitaria, l'appello si svolgerà come prova orale. |

10/02/2022 | 09:00 | GENOVA | Compitino | Tenendo conto dell'attuale situazione sanitaria, l'appello si svolgerà come prova orale. |

13/06/2022 | 09:00 | GENOVA | Orale | |

22/06/2022 | 15:00 | GENOVA | Scritto | |

29/06/2022 | 09:00 | GENOVA | Orale | |

07/07/2022 | 15:00 | GENOVA | Scritto | |

15/07/2022 | 09:00 | GENOVA | Orale | |

09/09/2022 | 15:00 | GENOVA | Scritto | |

16/09/2022 | 09:00 | GENOVA | Orale |