TEORIA DEI SEGNALI M - Z

Module SEGNALI DETERMINATI E ALEATORI

The course aims to provide students with basic knowledge of statistics, probability theory, deterministic signals, and subsequently random or stochastic signals. In relation to Dublin Descriptors 1 (Knowledge and understanding) and 2 (Applying knowledge and understanding), the course aims to give students a general understanding of simple problems described using statistical and probabilistic methods. Additionally, students will be enabled to understand how to characterize deterministic signals with appropriate mathematical tools. Finally, by combining the tools and approaches described above, students will come to understand the concept of a random or stochastic process and its characteristics, applying the acquired knowledge to solve real engineering problems. 

In relation to Dublin Descriptors 3 (Making judgments), 4 (Communication skills), and 5 (Learning skills), the objective of the course is for students to acquire the ability to analyze and understand the characteristics of deterministic and stochastic signals. The student will be able to deepen what has been learned during the course and use the basic knowledge as a starting point for further studies. Furthermore, upon passing the exam, students will acquire the ability to mathematically formalize the results of transformations of linear systems on deterministic and stochastic signals, and communicate the acquired knowledge to their peers clearly and effectively. Finally, students will understand and know how to formalize the transformations carried out by the basic components of a communication system, applying the aforementioned knowledge to solve real-world problems. 

As a result, students will become independent from the teacher, acquiring the ability to refine and deepen their knowledge autonomously and creatively. By the end of the course, students should have developed the ability for independent and critical investigation, as well as for the formalization of real-world problems using statistical methods (also through numerous exercises conducted during the course), and the ability to discuss and present the results of such studies. Finally, with the tools acquired during the course, the student will be able to autonomously continue studying other engineering disciplines, having also mastered statistical investigation tools.

The course, divided into two modules—one on “Elements of Probability and Statistics for ICT” (held during the first semester) and the other on “Deterministic and Random Signals” (held during the second semester)—is organized into lectures and exercises, both on the board and on the computer. In case of a COVID emergency, the lectures and exercises may be held on a designated online platform indicated by the university. If the course is delivered in a hybrid or remote mode, necessary changes may be introduced to the previously stated format to ensure the scheduled program, as outlined in the syllabus, is followed. The lectures are highly interactive, with contributions from both the instructor and students, who are invited to carry out exercises with the support of the instructor.

Finally, a series of seminars is usually scheduled at the end of the course, demonstrating the application of signal theory and spectral analysis to signal modulation and filtering using laboratory equipment (oscilloscope, filters, modulators/demodulators).

Module 2: “Deterministic and Random Signals”
Definition and examples of signals; elementary properties of signals; harmonic analysis of periodic signals; *amplitude and phase spectra and their properties; even, odd, alternating signals; synthesis of a signal from a limited number of harmonics.
*The Fourier integral; *properties of the Fourier transform; theorems on the Fourier transform (linearity, duality, delay, scaling, *modulation, derivation, integration, product, convolution); *Fourier transform of the generalized impulsive function, Dirac's delta function, and notable transforms; *periodization and Poisson's formulas; *sampling theorem.
*Concept of a “system” and signal transformation; properties of one-dimensional systems; *characterization and analysis of linear stationary systems (impulse response and frequency response); decibels; *cascade and parallel systems; *ideal filters: low-pass, high-pass, band-pass, band-reject filters; real filters; *bandwidth of a signal and a system; notes on distortions introduced by filters; *Parseval's theorem and energy spectral density; *power spectral density; *autocorrelation function; Wiener-Khintchine theorem; *power spectral density of periodic signals.
*Continuous-time random processes; *parametric random processes; first- and second-order statistical indices of a random process; *stationarity; filtering of a wide-sense stationary random process; power spectral density of a continuous-time stationary process; *white noise and continuous-time Gaussian random processes; *ergodicity.

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

Unless there is a COVID emergency, a midterm written exam takes place to assess the ability to solve problems described in statistical and probabilistic terms. The midterm exam takes place at the end of the first semester and lasts two hours. It consists of two exercises and two open-ended theoretical questions. If passed, the midterm exempts the student from the portion of the final exam related to Module 1 on Elements of Probability and Statistics for ICT. The grade obtained in the midterm contributes half of the final evaluation.

Unless there is a COVID emergency, the final exam is written and lasts two hours. It consists of two exercises and two open-ended theoretical questions. If the student has passed the midterm, the exercise and theoretical question concerning Module 1 will be replaced by an exercise and a question focused on Module 2.

Each exercise and each theoretical question is worth up to 10 points. The total score will be multiplied by 3 and divided by 4.

To pass any exam, it is necessary to obtain at least 10 points in the two exercises.

The theoretical questions may include the discussion of theorems. The proof of the theorems contributes to the grade, but it is not required to pass the exam.

Students who obtain a grade of 18 or higher on the written exam may take an oral exam. Depending on the outcome of the oral exam, the grade may increase or decrease by up to three points.

Finally, students who wish to do so may prepare and discuss up to three short papers, each of which can contribute one point to the final grade.