# SIGNAL THEORY

## Learning outcomes of the course unit

This course aims at introducing and developing the concepts of deterministic signal and random signal, as models for physical systems of interest in the engineering contexts (electronics, computer science, telecommunications and related subjects). Signal transfomrations are introduced, as models of various systems encountered in several areas of ICT (amplifiers, filters, transmission lines, modulators, samplers, etc.).

At the end of the course, the Student should:

- know the techniques for the analysis of signals in the frequency domain;

- being able to apply these techniques to the filtering an sampling of an analog signal;

- understand and being able to model problems in the context of probability theory;

- personally manage simple probabilistic models, and be able to compare them critically, with the tools of random variables;

- know and be able to communicate concepts related to random signal (mean parameters; power spectral density, stationarity,).

- be able to face the face and deepen autonomously the case-study of specific random processes (harmonic process, PAM signal, etc.).

This course aims at introducing and developing the concepts of deterministic signal and random signal, as models for physical systems of interest in the engineering contexts (electronics, computer science, telecommunications and related subjects). Signal transfomrations are introduced, as models of various systems encountered in several areas of ICT (amplifiers, filters, transmission lines, modulators, samplers, etc.).

At the end of the course, the Student should:

- know the techniques for the analysis of signals in the frequency domain;

- being able to apply these techniques to the filtering an sampling of an analog signal;

- understand and being able to model problems in the context of probability theory;

- personally manage simple probabilistic models, and be able to compare them critically, with the tools of random variables;

- know and be able to communicate concepts related to random signal (mean parameters; power spectral density, stationarity,).

- be able to face the face and deepen autonomously the case-study of specific random processes (harmonic process, PAM signal, etc.).

## Prerequisites

Knowledge of the fundamentals of Claculus, with specific reference to the algebra of complex numbers and their representation in the exponential form (and related Euler's forulae).

Knowledge of the fundamentals of Claculus, with specific reference to the algebra of complex numbers and their representation in the exponential form (and related Euler's forulae).

## Course contents summary

The course is divided in three parts:

- in the first part, we introduce deterministic signals and their analysis, both in the time- and in the frequency-domain. We shall analyze the trasformations that signals undergo through linear systems and through the sampling process;

- the second part is an introduction to the fundamentals of the theory of probability and random variables, with applications to engineering problems;

- the third part sums up the first two in the concept of stochastic process, as a model to study random signals and their transformations throgh systems.

The course is divided in three parts:

- in the first part, we introduce deterministic signals and their analysis, both in the time- and in the frequency-domain. We shall analyze the trasformations that signals undergo through linear systems and through the sampling process;

- the second part is an introduction to the fundamentals of the theory of probability and random variables, with applications to engineering problems;

- the third part sums up the first two in the concept of stochastic process, as a model to study random signals and their transformations throgh systems.

## Recommended readings

- A. Vannucci, "Segnali analogici e sistemi ineari", Pitagora Editrice, Bologna, 2003, ISBN: 88-371-1416-8.

- A. Bononi, G. Ferrari, "Introduzione a Teoria della probabilità e variabili aleatorie con applicazioni all'ingegneria e alle scienze", Soc. Editrice Esculapio, Bologna, aprile 2008, ISBN: 978-88-7488-257-1.

- A. Vannucci, "Esercizi d'esame di Teoria dei Segnali", Pitagora Editrice, Bologna, 2018, ISBN: 88-371-1811-2.

- A. Vannucci, "Segnali analogici e sistemi ineari", Pitagora Editrice, Bologna, 2003, ISBN: 88-371-1416-8.

- A. Bononi, G. Ferrari, "Introduzione a Teoria della probabilità e variabili aleatorie con applicazioni all'ingegneria e alle scienze", Soc. Editrice Esculapio, Bologna, aprile 2008, ISBN: 978-88-7488-257-1.

- A. Vannucci, "Esercizi d'esame di Teoria dei Segnali", Pitagora Editrice, Bologna, 2018. (in print)

## Teaching methods

This is a course of 9 credits (CFU), for which 72 hours of Class Lecturesare foreseen, to build up the understanding and critical processing of the subject matter.

Applications and exercises related to the presented topics are regularly proposed (via traditional or flipped classroom techniques) to develop application skills. Other assignments are given through the web learning platform Elly.

When foreseen by the long-term teaching plan of this University, a Tutor shall give guided exercises.

Teaching methods shall be adapted to the possible presence (detected according to laws and guidelines) of students with special needs and or disabilities.

This is a course of 9 credits (CFU), for which 72 hours of Class Lecturesare foreseen, to build up the understanding and critical processing of the subject matter.

Applications and exercises related to the presented topics are regularly proposed (via traditional or flipped classroom techniques) to develop application skills. Other assignments are given through the web learning platform Elly.

When foreseen by the long-term teaching plan of this University, a Tutor shall give guided exercises.

Teaching methods shall be adapted to the possible presence (detected according to laws and guidelines) of students with special needs and or disabilities.

## Assessment methods and criteria

The overall assessment of the learning outcomes foresees two tests:

1) a structured written test with 3 open questions, where the student shall demonstrate his/her ability to:

- analyze an analog signal and its possible transformations, in the time and frequency domain;

- model and solve a problem of probabiility theory, that possibly employs random variables;

- analyze a random signal and its possible filtering, by evaluating its moments and/or power spectrum

The duration of the written test is 2hours. The test is evaluated on a 0-30 scale, plus possible honors, in the case of top grades in all items together with an ppropriateness of language.

2) an oral test, consisting of a critical discussion about the topics developed during the course. The student shall demonstrate proper knowledge and ability to illustrate the topic, with sufficient accuracy in the language.

Students can optionally take two intermediate written tests- to take place halfway during the course and at the end of the course, respectively - that shall replace the overall assessment procedure above.

The first test is a sequence of 10 closed multiple choice questions, followed by two open questions, similar to those illustrated at point 1) above.

The second test is is ismply made up of two open questions, similar to those illustrated at point 1) above.

In case the student takes both intermediate tests, the overall evaluation shall be assessed without an oral test.ue prove, senza necessità di una prova orale successiva.

Assessment methods shall be adapted to the possible presence (detected according to laws and guidelines) of students with special needs and or disabilities.

The overall assessment of the learning outcomes foresees two tests:

1) a structured written test with 3 open questions, where the student shall demonstrate his/her ability to:

- analyze an analog signal and its possible transformations, in the time and frequency domain;

- model and solve a problem of probabiility theory, that possibly employs random variables;

- analyze a random signal and its possible filtering, by evaluating its moments and/or power spectrum

The duration of the written test is 2hours. The test is evaluated on a 0-30 scale, plus possible honors, in the case of top grades in all items together with an appropriateness of language.

2) an oral test, consisting of a critical discussion about the topics developed during the course. The student shall demonstrate proper knowledge and ability to illustrate the topic, with sufficient accuracy in the language.

Students can optionally take two intermediate written tests- to take place halfway during the course and at the end of the course, respectively - that shall replace the overall assessment procedure above.

The first test is a sequence of 10 closed multiple choice questions, followed by two open questions, similar to those illustrated at point 1) above.

The second test is is ismply made up of two open questions, similar to those illustrated at point 1) above.

In case the student takes both intermediate tests, the overall evaluation shall be assessed without an oral test.ue prove, senza necessità di una prova orale successiva.

Assessment methods shall be adapted to the possible presence (detected according to laws and guidelines) of students with special needs and or disabilities.