02OGGOA

A.A. 2023/24

Course Language

Inglese

Course degree

1st degree and Bachelor-level of the Bologna process in Ingegneria Informatica - Torino

Course structure

Teaching | Hours |
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Teachers

Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
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Teaching assistant

Context

SSD | CFU | Activities | Area context |
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ING-INF/03 | 8 | B - Caratterizzanti | Ingegneria delle telecomunicazioni |

2022/23

The class describes the main fundamental analysis and processing techniques for deterministic and random continuous-time signals (first part), and for deterministic and random discrete-time signals (second part). The topics are quite multidisciplinary in the sense that these notions and techniques are used in many of the classes that follow.

The class describes the main fundamental analysis and processing techniques for deterministic and random continuous-time signals (first part), and for deterministic and random discrete-time signals (second part). The topics are quite multidisciplinary in the sense that these notions and techniques are used in many of the classes that follow.

The specific knowledge and abilities that the student will acquire are:
- Knowledge of the classification of signals.
- Knowledge of frequency analysis for continuous-time signals.
- Knowledge of linear time-invariant (LTI) systems, as well as of their representation in the time and frequency domains.
- Knowledge of the basic types of signal filters.
- Knowledge of the analytic signals and systems representation and ability to use it properly.
- Knowledge of random signals (called random processes), of their statistical characterization and of their spectral representation.
- Ability to classify signals with respect to their properties.
- Ability to transform and analyze a signal in the time and frequency domains.
- Ability to classify and analyze a LTI system in the time and frequency domains.
- Ability to statistically describe a random process and to characterize its spectral properties, as well as its interactions with LTI systems.
- Knowledge of the techniques for passing from a continuous-time to discrete-time signal, and vice-versa.
- Knowledge of the techniques for digital processing of a signal in the frequency domain.
- Knowledge of the techniques for discrete-time processing of digital signals in the frequency domain.
- Knowledge of the techniques for analysis of LTI systems in discrete-time, and of the Z-transform.
- Knowledge of digital filters structures (FIR, IIR)
- Ability to pass from discrete time to continuous time signals, and vice-versa.
- Ability to process discrete-time signals and systems in the time and z-domain.
- Ability to analyze discrete-time LTI systems.

The specific knowledge and abilities that the student will acquire are:
- Knowledge of the classification of signals.
- Knowledge of frequency analysis for continuous-time signals.
- Knowledge of linear time-invariant (LTI) systems, as well as of their representation in the time and frequency domains.
- Knowledge of the basic types of signal filters.
- Knowledge of random signals (called random processes), of their statistical characterization and of their spectral representation.
- Ability to classify signals with respect to their properties.
- Ability to transform and analyze a signal in the time and frequency domains.
- Ability to classify and analyze a LTI system in the time and frequency domains.
- Ability to statistically describe a random process and to characterize its spectral properties, as well as its interactions with LTI systems.
- Knowledge of the techniques for passing from a continuous-time to discrete-time signal, and vice-versa.
- Knowledge of the techniques for digital processing of a signal in the frequency domain.
- Knowledge of the techniques for discrete-time processing of digital signals in the frequency domain.
- Knowledge of the techniques for analysis of LTI systems in discrete-time, and of the Z-transform.
- Knowledge of digital filters structures (FIR, IIR)
- Ability to pass from discrete time to continuous time signals, and vice-versa.
- Ability to process discrete-time signals and systems in the time and z-domain.
- Ability to analyze discrete-time LTI systems.

Fundamentals of Calculus (including trigonometric, exponential and logarithmic functions, with their properties). Fundamental notions of linear algebra, Euclidean spaces and the representation of their elements in terms of components vs. a basis. Complex analysis of functions in one or two variables. Fourier series, Fourier and Laplace transforms. First order linear differential equations. Probability theory: discrete and continuous random variables, probability density function, expectation operator. Geometric series and their convergence criteria.

Fundamentals of Calculus (including trigonometric, exponential and logarithmic functions, with their properties). Fundamental notions of linear algebra, Euclidean spaces and the representation of their elements in terms of components vs. a basis. Complex analysis of functions in one or two variables. Fourier series, Fourier and Laplace transforms. First order linear differential equations. Probability theory: discrete and continuous random variables, probability density function, expectation operator. Geometric series and their convergence criteria.

Topics dealt with in the class:
- Signal classification; energy and power (0.4 CFU)
- Linear and inner-product spaces, signal spaces, signal canonical representation and approximants (0.8 CFU)
- Fourier series and transform (0.8 CFU)
- Linear Time Invariant (LTI) systems, impulse response and transfer function (1 CFU)
- Energy spectrum and autocorrelation function. Periodic signals and power spectral density (1 CFU)
- Random processes (2 CFU)
- Sampling theorem (0.4 CFU)
- Discrete time signals: basic operations, energy and power (0.3 CFU)
- Discrete time Fourier transform: circular convolution, discrete time Fourier transform (0.7 CFU)
- Discrete time LTI systems: Z transform based analysis (0.6 CFU)
(CFUs are indicative – variations are possible.)

Topics dealt with in the class:
- Signal classification; energy and power (0.4 CFU)
- Linear and inner-product spaces, signal spaces, signal canonical representation and approximants (0.8 CFU)
- Fourier series and transform (0.8 CFU)
- Linear Time Invariant (LTI) systems, impulse response and transfer function (1 CFU)
- Energy spectrum and autocorrelation function. Periodic signals and power spectral density (1 CFU)
- Random processes (2 CFU)
- Sampling theorem (0.4 CFU)
- Discrete time signals: basic operations, energy and power (0.3 CFU)
- Discrete time Fourier transform: circular convolution, discrete time Fourier transform (0.7 CFU)
- Discrete time LTI systems: Z transform based analysis (0.6 CFU)
(CFUs are indicative – variations are possible.)

Theoretical topics are dealt with in regular lectures. Regarding problem-solving, either the teacher solves problems in class on the topics introduced during the lecture, or the students work independently on the suggested problems with guidance from the teacher.

Theoretical topics are dealt with in regular lectures. Regarding problem-solving, either the teacher solves problems in class on the topics introduced during the lectures, or the students work independently on the suggested problems with guidance from the teacher.

1. P. Poggiolini and M. Visintin, Class Notes on Signal Analysis and Processing (downloadable from the course portal).
For further (optional) reading:
2. A. Papoulis e S. U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2002.
3. A.V.Oppenheim R.W.Schafer: Discrete-Time Signal Processing, Prentice-Hall (any edition)
4. Luca Mesin, Introduction to signal theory, CLUT.
Available in Italian, again as optional material:
5. L. Lo Presti e F. Neri, L'analisi dei segnali, CLUT, 1992.
6. L. Lo Presti e F. Neri, Introduzione ai processi casuali, CLUT, 1992.
7. M. Laddomada e M. Mondin, Elaborazione numerica dei segnali, Pearson, 2007.

1. P. Poggiolini and M. Visintin, Class Notes on Signal Analysis and Processing (downloadable from the course portal).
For further (optional) reading:
2. A. Papoulis e S. U. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2002.
3. A.V.Oppenheim R.W.Schafer: Discrete-Time Signal Processing, Prentice-Hall (any edition).
4. Luca Mesin, Introduction to signal theory, CLUT.

...
The final exam consists of a mandatory written test and an optional oral test.
The written test lasts two hours and is made up of three to five questions or problems that may involve theoretical aspects, proofs of results, or solving computational problems. The written test is "closed books", although students are given a standard "table of formulas" which they can consult. Students are allowed to use a non-programmable non-graphic pocket calculator. The device must be stand-alone and not consist of an app on a smart-phone, tablet, or similar. Any device that can connect to the internet is strictly forbidden.
The questions and problems of the written test will deal with all three main sections of the class: deterministic time-continuous signals and linear systems, discrete-time signals and linear systems, random processes.
The written test is meant to verify that students have acquired the knowledge of the fundamental concepts of Signal Theory and related Systems and the skills needed to classify, manipulate and process them.
The written test maximum grade is 30/30.
The optional oral exam can be taken by students whose written test is sufficient (18/30 or higher). Besides further probing the students’ knowledge, it will also focus on their ability to use the appropriate technical terms and their promptness in providing the answers.
The oral test maximum grade is 30/30.
The final exam grade is awarded by summing the following:
- the written exam grade, multiplied times 9/10
- the optional oral exam grade, multiplied by 1/10
Particularly brilliant students may be awarded the grade 30/30 with “lode”.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

The final exam consists of a mandatory written test and an optional oral test.
The written test lasts approximately two hours and consists of questions that may involve theoretical aspects, proofs of results, and solving computational problems. In case of computational problems, the mathematical steps used to get to the solution may have to be submitted. The written test is "closed books". Students are given a standard "table of formulas" which they can consult. Students are allowed to use the scientific calculator embedded in the exam application software. The questions and problems of the written test deal with all three main sections of the course: deterministic time-continuous signals and linear systems, discrete-time signals and linear systems, random processes. The written test is meant to verify that students have acquired the knowledge of the fundamental concepts of signal theory and related systems and the skills needed to classify, manipulate and process them. The written test maximum grade is 30/30. Students can withdraw from the exam after learning about their written test grade.
The optional oral exam can be taken by students whose written test is sufficient (18/30 or higher). Besides further probing the students’ knowledge, it will also focus on their ability to use the appropriate technical terms and their promptness in providing the answers. The oral test grade ranges from -5 to +5.
The final exam grade is awarded by summing the following:
- the written exam grade
- the optional oral exam grade, from -5 to +5
Particularly brilliant students may be awarded the grade 30/30 with “lode”.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

© Politecnico di Torino

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY