01DSKBG

A.A. 2023/24

Course Language

Inglese

Course degree

Course structure

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Teachers

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Teaching assistant

Context

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2022/23

The course gives the basis for the processing of random signals (random processes), which represent the most common type of signals in the fields of the Communication and Computer Networks Engineering, as well as, in general, in the fields of engineering where random quantities are measured. We consider both the case of deterministic signals affected by noise, generated for instance by the measurement system, as well as that of signals whose nature is inherently random, such as 1/f noise. The course begins by reviewing the foundations of discrete-time random processes, particularly by discussing the quantities that describe them, such as the autocorrelation function, the power spectrum, and the time-frequency spectrum, useful for signals whose frequency content changes with time. We consider both stationary and nonstationary random processes commonly encountered in nature. We then give the basis of estimation theory, and we derive and discuss the main estimators for the mean, variance, autocorrelation function, and power spectrum of stationary and nonstationary random processes. Furthermore, we introduce random dynamical systems and we derive the Kalman filter, which allows their optimal estimation. Finally, we introduce the basis of detection theory and we illustrate how to design a detector according to the Neyman-Pearson criterion. Half of the course takes place in the LAIB laboratories, where students implement and characterize in the Matlab environment all of the methods discussed during the lectures.

In this course we give the basis for processing random signals (random processes), which represent the most common type of signals in the fields of Communications Engineering, as well as in all of the fields of Engineering where random quantities are measured. We consider both the case of deterministic signals affected by noise, generated for instance by the measurement system, as well as that of signals whose nature is inherently random, such as 1/f noise. We begin by reviewing the foundations of discrete-time random processes, particularly by discussing the quantities that describe them, such as the autocorrelation function, the power spectrum, and the time-frequency spectrum, useful for signals whose frequency content changes with time. We consider both stationary and nonstationary random processes commonly encountered in nature. We then give the basis of estimation theory, and we derive and discuss the main estimators for the mean, variance, autocorrelation function, and power spectrum of stationary and nonstationary random processes. Furthermore, we introduce random dynamical systems and we derive the Kalman filter, which allows their optimal estimation. Finally, we introduce the basis of detection theory and we illustrate how to design a detector according to the Neyman-Pearson criterion. Half of the course takes place in the LAIB laboratories, where students implement and characterize in the Matlab environment all of the methods discussed during the lectures.

1. Knowledge of the foundations of discrete-time random processes
2. Knowledge of the basis of time-frequency analysis
3. Knowledge of the basis of estimation theory
4. Knowledge of the basis of Kalman filtering
5. Knowledge of the basis of detection theory
6. Ability to classify stationary and nonstationary random processes
7. Ability to design estimation algorithms for signals affected by noise
8. Ability to use the Kalman filter for the estimation of random processes and systems
9. Ability to design a detector
Judgment and communication skills are strengthened during the laboratories thank to the continual interaction with the teacher. To improve the learning skill, we teach how to search scientific and tutorial references on the main online search engines, such as IEEE XPlore.

1. Knowledge of the foundations of discrete-time random processes
2. Knowledge of the basis of time-frequency analysis
3. Knowledge of the basis of estimation theory
4. Knowledge of the basis of Kalman filtering
5. Knowledge of the basis of detection theory
6. Ability to classify stationary and nonstationary random processes
7. Ability to design estimation algorithms for signals affected by noise
8. Ability to use the Kalman filter for the estimation of random processes and systems
9. Ability to design a detector
Judgment and communication skills are strengthened during the laboratories thank to the continual interaction with the teacher. To improve the learning skill, we teach how to search scientific and tutorial references on the main online search engines, such as IEEE XPlore.

The student must know the following concepts of probability theory and signal processing:
1. Random variable
2. Probability density function
3. Mean
4. Variance
5. Frequency analysis
6. Linear time-invariant (LTI) systems
However, at the beginning of the course these notions are reviewed with an intuitive approach.

The student must know the following concepts of probability theory and signal processing:
1. Random variable
2. Probability density function
3. Mean
4. Variance
5. Frequency analysis
6. Linear time-invariant (LTI) systems
However, at the beginning of the course these notions are reviewed with an intuitive approach.

Introduction. Discrete-time random processes (15 hours)
Nonstationary random processes (9 hours)
Introduction to estimation theory (9 hours)
Spectral estimation (6 hours)
Time-frequency analysis (6 hours)
The Kalman filter (9 hours)
Introduction to detection theory (6 hours)

Discrete-time signals and systems (15 hours)
Nonstationary random processes (9 hours)
Introduction to estimation theory (9 hours)
Spectral estimation (6 hours)
Time-frequency analysis (6 hours)
The Kalman filter (9 hours)
Introduction to detection theory (6 hours)

Half of the course takes place in the LAIB laboratories, where students implement and characterize in the Matlab environment all of the methods discussed during the lectures.

Half of the course takes place in the LAIB laboratories, where students implement and characterize in the Matlab environment all of the methods discussed during the lectures.

[1] D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing, Artech House, 2011.
[2] L. Cohen, Time-frequency analysis, Prentice Hall, 1995.
[3] A. Gelb (Editor), Applied Optimal Estimation, The MIT Press, 1974.
[4] Steven M. Kay, Fundamentals of Statistical signal processing: Estimation Theory, Prentice Hall,1993
[5] Steven M. Kay, Fundamentals of Statistical signal processing: Detection Theory, Prentice Hall,1993

[1] D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing, Artech House, 2011.
[2] L. Cohen, Time-frequency analysis, Prentice Hall, 1995.
[3] A. Gelb (Editor), Applied Optimal Estimation, The MIT Press, 1974.
[4] Steven M. Kay, Fundamentals of Statistical signal processing: Estimation Theory, Prentice Hall, 1993
[5] Steven M. Kay, Fundamentals of Statistical signal processing: Detection Theory, Prentice Hall, 1993

...
The written exam with a duration of one hour is based on approximately 12-15 multiple choice questions which span the content of both the lectures and the laboratories. Every correct answer gives a positive score, which is identical for all of the questions. The final mark is the sum of all of the positive scores. During the exam it is not possible to use support material, such as notes or books. The highest mark which can be obtained at the written exam is 30 cum laude. If the number of students booked for the exam is smaller or equal than 10, the written exam can be replaced by an oral exam of approximately 30 minutes, focused on the topics taught both during the lectures and at the laboratories. The highest mark which can be obtained with the oral exam is 30 cum laude.
The final mark for the Signal, image and video processing and learning course is the arithmetic average of the mark for this course (Signal processing: methods and algorithms) and of the mark for the Image and video processing and learning course. The highest final mark is 30 cum laude.

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 written exam with a duration of one hour is based on approximately 12-15 multiple choice questions which span the content of both the lectures and the laboratories. Every correct answer gives a positive score, which is identical for all of the questions. The final mark is the sum of all of the positive scores. During the exam it is not possible to use support material, such as notes or books. The highest mark which can be obtained at the written exam is 30 cum laude. If the number of students booked for the exam is smaller or equal than 10, the written exam can be replaced by an oral exam of approximately 30 minutes, focused on the topics taught both during the lectures and at the laboratories. The highest mark which can be obtained with the oral exam is 30 cum laude.
The final mark for the Signal, image and video processing and learning course is the arithmetic average of the mark for this course (Signal processing: methods and algorithms) and of the mark for the Image and video processing and learning course. The highest final mark is 30 cum laude.

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.

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Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY