Signal theory
Academic Year 2023/2024 - Teacher: Giacomo MORABITOExpected Learning Outcomes
Knowledge and understanding
The knowhow achieved through the course will allow students to go deeper, when needed, in different topics relevant to the course.
Examples include, probability theory and the analysis of random signals in both the time and frequency domain.
Applying knowledge and understanding
Applying the competences achieved through the course, students will be able to model practical problems exploiting the specific tools regarding the analysis of random variables and stochastic processes.
Objective of this course is to provide knowledge about: fundamentals of probability theory, random variables, periodic and aperiodic deterministic signals, random processes, filtering of deterministic signals and random signals.
At the end the student will be able to
- model random experiments and derive their characteristic parameters making use, if appropriate, of random variables
- analyze signals (both determined and random) in time and frequency domains
- derive characteristic features of signals (both deterministic and random) in output of linear time-invariant systems starting from the characterization of the signals and of the system itself
Autonomia di giudizio (Making judgements)
Abilità comunicative (Communication skills)
Capacità di apprendimento (Learning skills)
Making judgments
The student can critically analyze problems in the context of signal theory and can apply the most appropriate solution techniques. Such capabilities are acquired in the context of exercises executed in class.
Communication skills
The student can communicate the fundamental concepts regarding Signal Theory both in oral and written manner using mathematical language. Such ability is developed in class and evaluated during the exams.
Learning skills
The student can read and understand scientific and technical documents in the context of Signal Theory. Such ability is acquired through individual study of the suggested text.
Course Structure
Lectures for theory and exercises.
Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.
Required Prerequisites
Solutions of integrals, derivatives, disequalities, complex numbers, elementary electric circuits.
Students are requested to take a self assessment test at the beginning of the course.
Attendance of Lessons
Detailed Course Content
Deterministic signals: fundamentals, properties, representation in the time and frequency domain, Fourier transforms, systems, linear and time invariant systems, signal filtering.
Probability theory: fundamentals, random experiments and probability laws, random variables, transformation of random variables, systems of random variables.
Random signals: fundamentals, properties, characterization in the time and frequency domains, random signal filtering, noise, Markov processes
Textbook Information
M. Luise, G. Vitetta. Teoria dei segnali. McGraw Hill.
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Segnali determinati: concetti e loro applicazione (15 ore) | [1] |
| 2 | Segnali determinati: dimostrazioni e approfondimenti teorici (11 ore) | [1] |
| 3 | Teoria della probabilità: concetti e loro applicazione (25 ore) | [1] |
| 4 | Teoria della probabilità: dimistrazioni e approfondimenti teorici (10 ore) | [1] |
| 5 | Segnali aleatori: concetti e loro applicazione (11 ore) | [1] |
| 6 | Segnali aleatori: dimostrazioni e approfondimenti teorici (7 ore) | [1] |
Learning Assessment
Learning Assessment Procedures
Usually, the exam is written (mandatory) and oral (optional).
The written exam consists of two exercises and two theoretical questions.
Exercises and answers to theoretical questions will be evaluated separately with a vote from 0 to 20 each.
In order to pass the exam it is necessary to obtain at least 8/20 in the exercises.
The proposed vote is the mean (normalized to 30) of what has been obtained in the exercises and theory.
Students willing to increase their evaluation can take a further oral exam that may result in the increase or decrease of the vote of 3 points (at most).
Duration of the written exam is 2 hours.
To ensure equal opportunities and in compliance with current laws, interested students may request a personal interview in order to plan any compensatory and/or dispensatory measures based on educational objectives and specific needs. Students can also contact the CInAP (Centro per l’integrazione Attiva e Partecipata - Servizi per le Disabilità e/o i DSA) referring teacher within their department.
In particular cases we may be forced to carry examination out on line. In such a case, the exam will be oral and the students will be requested to do two exercises. The discussion of the solutions will be the starting points for addressing theoretical aspects.