TEORIA DEI SEGNALI A - LModule SEGNALI DETERMINATI E ALEATORI
Academic Year 2025/2026 - Teacher: Alfio LOMBARDOExpected Learning Outcomes
Signal Theory
The course aims to provide students with the basics of signals theory and random
signals theory.
In relation to the Dublin Descriptors 1 (Knowledge and understanding) and 2 (Applying knowledge and
understanding), the course aims to provide students with the capability of understanding how to
characterize deterministic signals with suitable mathematical tools. Finally, from the combination of the
tools and approaches described in both modules of this course, students will come to understand the concept of random
processes and their characteristics, thus applying the acquired knowledge to the solution of real
engineering problems.
In relation to the Dublin Descriptors 3 (Making judgemements), 4 (Communication skills) and 5 (Learning
skills), the aim of the teaching is that students acquire the ability to analyze and understand the
characteristics of deterministic and random signals. The students will be able to deepen what they have
learned in the course, and use the basic knowledge as a starting point for subsequent studies.
Furthermore, upon passing the exam, students will acquire the ability to mathematically formalize the
results of transformations of linear systems on determined and random signals with the ability to
communicate the acquired knowledge to others in a clear and complete way. Finally, students will
understand and will be able to formalize the transformations made by the basic components of a
communication system by applying the above knowledge to the solution of real problems. The student
will therefore become independent from the teacher, acquiring the ability to refine and deepen their
knowledge in an autonomous and original way. Upon completion of the course the students must gain
independent and critical investigation skills as well as ability to formalize through statistical methods
some real problems (also through the help of numerous exercises carried out during the course), as well
as the ability to discuss and present the results of such studies. Finally, at the end of the course, the
students will be able to continue independently their study of other engineering disciplines with the
ability to appropriately use statistical tools.
Course Structure
The course consists of lectures and exercises both on the blackboard and the computer. In case of COVID
emergency, lectures will be provided through an appropriate computer platform.
The final exam could be eventually done remotely in case of COVID contingency.
The theorethical lessons are taught by the teacher while the exercises are both done by the teacher and
the students who are invited to perform, with the support of the teacher, the tests. Finally, seminars are usually scheduled at the end of the course in which the application
of signal theory and spectral investigation to the modulation and filtering of signals with laboratory
equipment (oscilloscope filters, modulators / demodulators) is demonstrated.
Should teaching be carried out in mixed or only remote mode, it could be needed to introduce some
necessary variations as compared to what has been foreseen and reported in the syllabus.
Required Prerequisites
Ability to solve integrals, derivatives and inequalities, knowledge of complex numbers, elementary electrical circuits
elementary electrical circuits of the resistive and RC type.
Students are required to take a self-assessment test at the beginning of the course.
Detailed Course Content
Part 1. Analysis of Periodic and Continuous Signals
*Definitions and examples of signals; elementary properties of signals; *Harmonic analysis of periodic signals; *amplitude and phase spectra of signals and their properties; synthesis of a signal from a finite number of harmonics.* Fourier integral;* Fourier transform; Fourier transform theorems (linearity, duality, delay, scale change, *modulation, derivation, integration, product, convolution); *Dirac delta generalized function and its transformation; *Periodicization of a signal and Poisson formulas; *Sampling theorem.
Part 2. Linear and stationary systems
*Definition of "system" and transformation of a signal through a system; properties of one-dimensional systems; *characterization and analysis of stationary linear systems (impulse response and frequency response); decibels;* cascading and parallel systems; Ideal filters ( low pass, high pass, band pass, delete band; real filters; signal bandwidth; distortion due to the filtering process; *Parseval theorem and spectral energy density;*spectral power density; *autocorrelation function; Wiener-Khintchine theorem.
Part 3. Elementary transformations of random signals
*Random processes; *parametric random processes; *Stationary processes; Filtering of a stationary random process; spectral power density of a stationary random process; *White noise and thermal noise; *Ergodicity of a process.
*minimum required arguments
Textbook Information
1) Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill
2) Leon Couch: Fondamenti di Telecomunicazioni, VII Ed. Pearson, Prentice Hall
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | esempi di segnali e proprieta’ elementari; Analisi armonica dei segnali periodici; spettri di ampiezza e fase e loro proprieta’; segnali pari, dispari, alternativi; sintesi di un segnale a partire da un numero limitato di armoniche (10 ore) | Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill |
| 2 | L’integrale di Fourier; proprieta’ della trasformata di Fourier e relativi teoremi; trasformata di Fourier della funzione generalizzata impulsiva di Dirac e trasformate notevoli; Periodicizzazione e formule di Poisson; Teorema del campionamento (15ore) | Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill |
| 3 | Concetto di “sistema” e trasformazione di un segnale; proprieta’ dei sistemi monodimensionali; caratterizzazione e analisi dei sistemi lineari stazionari (risposta impulsiva e risposta in frequenza); ; decibel; sistemi in cascata e in parallelo (10 ore) | Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill |
| 4 | Filtri ideali passa_basso, passa_alto, passa_banda,elimina_banda; flltri reali; banda di un segnale e di un sistema; cenni sulle distorsioni introdotte da filtri (4 ore) | Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill |
| 5 | Teorema di Parseval e densita’ spettrale di energia; densita’ spettrale di potenza; funzione di autocorrelazione; teorema di Wiener-Khintchine; densita’ spettrale di potenza di segnali periodici (8ore) | Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill |
| 6 | Processi aleatori(PA) tempo continuo, parametrici; Indici di un PA; Stazionarietà; Filtraggio di PA stazionario in senso lato; densità spettrale di potenza di PA continuo stazionario; PA gaussiani e Rumore bianco; Ergodicità; (12ore) | Marco Luise, Giorgio Vitetta: Teoria dei Segnali, Mc Graw Hill |
Learning Assessment
Learning Assessment Procedures
"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 write and discuss the essays proposed during the course, each of which may contribute to the final assessment.