The class describes the main fundamental analysis and processing techniques for deterministic and random continuous-time signals (first part), and for deterministic and random discrete-time signals (second part). The topics are quite multidisciplinary in the sense that these notions and techniques are used in many of the classes that follow. For the final project, each student will develop a simple Matlab simulator of a communication link.

The specific knowledge and abilities that the student will acquire are: - Knowledge of the classification of signals. - Knowledge of frequency analysis for continuous-time signals. - Knowledge of linear time-invariant (LTI) systems, as well as of their representation in the time and frequency domains. - Knowledge of the basic types of signal filters. - Knowledge of the analytic signals and systems representation and ability to use it properly. - Knowledge of random signals (called random processes), of their statistical characterization and of their spectral representation. - Ability to classify signals with respect to their properties. - Ability to transform and analyze a signal in the time and frequency domains. - Ability to classify and analyze a LTI system in the time and frequency domains. - Ability to statistically describe a random process and to characterize its spectral properties, as well as its interactions with LTI systems. - Knowledge of the techniques for passing from a continuous-time to discrete-time signal, and vice-versa. - Knowledge of the techniques for digital processing of a signal in the frequency domain. - Knowledge of the techniques for discrete-time processing of digital signals in the frequency domain. - Knowledge of the techniques for analysis of LTI systems in discrete-time, and of the Z-transform. - Knowledge of digital filters structures (FIR, IIR) - Ability to pass from discrete time to continuous time signals, and vice-versa. - Ability to process discrete-time signals and systems in the time and z-domain. - Ability to analyze discrete-time LTI systems. The final project will allow the student - to get a better understanding of the concepts of random process, of stationarity, cyclostationarity and ergodicity - to practically learn the structure of the communication link - to improve critical thinking - to acquire the ability to write report - to improve the ability to communicate ideas and methods, and to critically comment the results.

Fundamentals of Calculus (including trigonometric, exponential and logarithmic functions, with their properties). Fundamental notions of linear algebra, Euclidean spaces and the representation of their elements in terms of components vs. a basis. Complex analysis of functions in one or two variables. Fourier series, Fourier and Laplace transforms. First order linear differential equations. Probability theory: discrete and continuous random variables, probability density function, expectation operator. Geometric series and their convergence criteria. Fundamental notions of computer programming in Matlab (TM).

Topics dealt with in the class: - Signal classification; energy and power (0.4 CFU) - Linear and inner-product spaces, signal spaces, signal canonical representation and approximants (0.8 CFU) - Fourier series and transform (0.8 CFU) - Linear Time Invariant (LTI) systems, impulse response and transfer function (1 CFU) - Analytic (complex) signals and systems representation (0.4 CFU). - DSB (Double-Side Band) and AM (Amplitude Modulation) Transmission Systems, PLL (Phase-Locked Loop), (1 CFU) - Energy spectrum and autocorrelation function. Periodic signals and power spectral density (1 CFU) - Random processes (2 CFU) - Sampling theorem (0.4 CFU) - Discrete time signals: basic operations, energy and power (0.3 CFU) - Discrete time Fourier transform, circular convolution, discrete time Fourier transform (0.9s CFU) - Discrete time LTI systems: time and frequency analysis, Z transform based analysis (1 CFU) (CFUs are indicative – variations are possible.)

Theoretical topics are dealt with in regular lectures. Regarding problem-solving, the teachers solve problems in class on the topics introduced during the lectures. The Final Project will be introduced in class and explained in detail in an interactive fashion.

1. P. Poggiolini and M. Visintin, Class Notes on Signal Analysis and Processing (downloadable from the course portal). For further (optional) reading: 2. A. Papoulis e S. U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2002. 3. A.V.Oppenheim R.W.Schafer: Discrete-Time Signal Processing, Prentice-Hall (any edition) 4. Luca Mesin, Introduction to signal theory, CLUT. Available in Italian, again as optional material: 5. L. Lo Presti e F. Neri, L'analisi dei segnali, CLUT, 1992. 6. L. Lo Presti e F. Neri, Introduzione ai processi casuali, CLUT, 1992. 7. M. Laddomada e M. Mondin, Elaborazione numerica dei segnali, Pearson, 2007.

Modalità di esame: Prova orale facoltativa; Prova scritta in aula tramite PC con l'utilizzo della piattaforma di ateneo;

Exam: Optional oral exam; Computer-based written test in class using POLITO platform;

... The final exam consists of a mandatory written test, a mandatory project and report and an optional oral test. The written test lasts two hours and is made up of three to five questions or problems that may involve theoretical aspects, proofs of results, or solving computational problems. The written test is "closed books", although students are given a standard "table of formulas" which they can consult. Students are allowed to use a non-programmable non-graphic pocket calculator. The device must be stand-alone and not consist of an app on a smart-phone, tablet, or similar. Any device that can connect to the internet is strictly forbidden. The questions and problems of the written test will deal with all three main sections of the class: deterministic time-continuous signals and linear systems, discrete-time signals and linear systems, random processes. The written test is meant to verify that students have acquired the knowledge of the fundamental concepts of Signal Theory and related Systems and the skills needed to classify, manipulate and process them. The written test maximum grade is 30/30. The optional oral exam can be taken by students whose written test is sufficient (18/30 or higher). Besides further probing the students’ knowledge, it will also focus on their ability to use the appropriate technical terms and their promptness in providing the answers. The oral test maximum grade is 30/30. The final project is compulsory and consists of developing the Matlab code that implements a simple application of the methods and techniques learned in the course. The report should concisely and clearly: - describe the methodology used to solve the problem - illustrate the structure of the code written to implement the solution - show some of the main results and discuss them. It is meant to assess the ability of the students to confront a practical design problem on their own and to show their soft-skills proficiency (in particular, writing skills). The final project maximum grade is 30/30. The final exam grade is awarded by summing the following: - the written exam grade, multiplied times 7/10 - the final project grade, multiplied by 2/10 - the optional oral exam grade, multiplied by 1/10 However, it is mandatory to have a sufficient written test grade (18/30 or higher) to pass the exam, irrespective of the final project grade. Particularly brilliant students may be awarded the grade 30/30 with “lode”.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.