|SCIENTIFIC DISCIPLINARY SECTOR||ING-INF/03|
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.
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.
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.
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)
Noise and analog modulations
PAM on noisy channels
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).
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.
Office hours: By appointment
ALDO GRATTAROLA (President)
GABRIELE MOSER (President Substitute)
All class schedules are posted on the EasyAcademy portal.
The exam consists of a written test and an oral test. The written test can also be dealt with by two small parts, relating to the program carried out in the first and second semester. Written tests consist of solving problems.
The marks of the written and oral tests are considered both for the determination of the final grade, according to a non-mathematical criterion that holds account of the overall evaluation of the candidate, also in continuity with the previous history of the course.
Students with learning disorders ("disturbi specifici di apprendimento", DSA) will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the delegate of the Engineering courses in the Committee for the Inclusion of Students with Disabilities.