TEORIA DEI SEGNALI A - LModule ELEMENTI DI PROBABILITA' E STATISTICA PER L'ICT
Academic Year 2024/2025 - Teacher: CHRISTIAN GRASSOExpected Learning Outcomes
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.
Course Structure
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).
Required Prerequisites
Attendance of Lessons
Detailed Course Content
Data collection and descriptive statistics, statistical inference and probabilistic models, *populations and samples.
*Data organization (frequency tables and charts, relative frequency tables and charts, histograms, ogives, stem and leaf plots), *measures that summarize data (mean, median, sample mode, variance, standard deviation, sample percentiles, and box plots), *Chebyshev's inequality, *normal samples, *bivariate data sets.
*Random experiment; probability, *Bayes' theorem; *total probability theorem; *random variables; *probability density function and cumulative distribution of notable random variables; *transformation of a random variable; *characteristic indices of a distribution; *Gaussian random variable; *other notable random variables; pairs of random variables; *central limit theorem.
*Maximum likelihood estimators, *confidence intervals, *estimates for the difference between the means of two normal populations, *Bayesian estimators.
Textbook Information
1) Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill
2) Sheldon M. Ross: Probabilità e statistica per l’ingegneria e le scienze, Apogeo
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Data collection and descriptive statistics, statistical inference and probabilistic models, populations and samples | Sheldon M. Ross: Probabilità e statistica per l’ingegneria e le scienze, Apogeo |
| 2 | Data organization (frequency tables and charts, relative frequency tables and charts, histograms, ogives, stem and leaf plots), measures that summarize data (mean, median, sample mode, variance, standard deviation, sample percentiles, and box plots), Chebyshev's inequality, normal samples, bivariate data sets | Sheldon M. Ross: Probabilità e statistica per l’ingegneria e le scienze, Apogeo |
| 3 | Probability, Bayes' and total probability theorems; random variables, PDF and CDF functions, and moments; random variable (RV) transformation; pairs of RVs; Gaussian random variable; central limit theorem | Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill |
| 4 | Maximum likelihood estimators, confidence intervals, estimates for the difference between the means of two normal populations, Bayesian estimators, examples | Sheldon M. Ross: Probabilità e statistica per l’ingegneria e le scienze, Apogeo |
Learning Assessment
Learning Assessment Procedures
Unless there is a COVID emergency, a midterm exam is usually held to test the ability to address problems described in statistical and probabilistic terms. The midterm takes place at the end of the first semester and lasts two hours. It consists of two exercises and two open-ended questions. If passed, the midterm exempts the student from the exam for Module 1 of the course on "Elements of Probability and Statistics for ICT." The grade from the midterm counts for 1/2 of the final evaluation.
It is possible to earn the course credits in two ways:
- Passing a single exam covering topics from both modules.
- Passing two separate exams, each focused on one of the modules. In this case, the final grade will be the average (rounded up) of the grades obtained in the two exams.
Both the single exam and the two exams related to the two modules last two hours and include two exercises and two open-ended theoretical questions.