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Signal processing: methods and algorithms
01QWFBG
A.A. 2020/21
Course Language
Inglese
Degree programme(s)
Master of science-level of the Bologna process in Communications And Computer Networks Engineering (Ingegneria Telematica E Delle Comunicazioni) - Torino
Course structure
| Teaching | Hours |
|---|---|
| Lezioni | 30 |
| Esercitazioni in laboratorio | 30 |
Lecturers
| Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
|---|---|---|---|---|---|---|---|
| Galleani Lorenzo | Professore Associato | IINF-03/A | 30 | 0 | 30 | 0 | 10 |
Co-lectures
Context
| SSD | CFU | Activities | Area context | ING-INF/03 | 6 | B - Caratterizzanti | Ingegneria delle telecomunicazioni |
|---|
2020/21
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.
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.
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)
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)
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. If the COVID-19 emergency will prevent access to the LAIBs, the Matlab laboratories will be carried out on a web platform.
[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
Modalità di esame: Prova orale facoltativa; Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo;
The online exam with the Exam platform and the Respondus tool has a duration of two hours, it is based on approximately 15-20 multiple choice questions which span the content of both the lectures and the laboratories, and it aims at verifying all of the Expected Learning Outcomes previously indicated. Every correct answer gives a positive score, 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. Examples of multiple choice questions will be made available on the course web page. If the number of students booked for the exam is smaller or equal than 10, the exam based on Exam+Respondus can be replaced by an oral exam through a web platform (such as Skype or Zoom) 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.
Exam: Optional oral exam; Computer-based written test using the PoliTo platform;
The online exam with the Exam platform and the Respondus tool has a duration of two hours, it is based on approximately 15-20 multiple choice questions which span the content of both the lectures and the laboratories, and it aims at verifying all of the Expected Learning Outcomes previously indicated. Every correct answer gives a positive score, 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. Examples of multiple choice questions will be made available on the course web page. If the number of students booked for the exam is smaller or equal than 10, the exam based on Exam+Respondus can be replaced by an oral exam through a web platform (such as Skype or Zoom) 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.
Modalità di esame: Test informatizzato in laboratorio; Prova orale facoltativa; Prova scritta tramite PC con l'utilizzo della piattaforma di ateneo;
The online exam with the Exam platform and the Respondus tool has a duration of two hours, it is based on approximately 15-20 multiple choice questions which span the content of both the lectures and the laboratories, and it aims at verifying all of the Expected Learning Outcomes previously indicated. Every correct answer gives a positive score, 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. Examples of multiple choice questions will be made available on the course web page. If the number of students booked for the exam is smaller or equal than 10, the exam based on Exam+Respondus can be replaced by an oral exam through a web platform (such as Skype or Zoom) 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 onsite exam is also based on the Exam platform and the Respondus tool, except that the students will access these tools from the IT laboratories at Politecnico di Torino. All of the details explained for the online tests apply to the onsite test. If the number of students booked for the exam is smaller or equal than 10, the multiple choice exam based on Exam+Respondus can be replaced by an oral exam of approximately 30 minutes focused on the topics taught both during the lectures and at the laboratories, which takes place on a web platform (such as Skype or Zoom) in the online case, and in the Politecnico di Torino premises in the onsite case.
Exam: Computer lab-based test; Optional oral exam; Computer-based written test using the PoliTo platform;
The online exam with the Exam platform and the Respondus tool has a duration of two hours, it is based on approximately 15-20 multiple choice questions which span the content of both the lectures and the laboratories, and it aims at verifying all of the Expected Learning Outcomes previously indicated. Every correct answer gives a positive score, 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. Examples of multiple choice questions will be made available on the course web page. If the number of students booked for the exam is smaller or equal than 10, the exam based on Exam+Respondus can be replaced by an oral exam through a web platform (such as Skype or Zoom) 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 onsite exam is also based on the Exam platform and the Respondus tool, except that the students will access these tools from the IT laboratories at Politecnico di Torino. All of the details explained for the online tests apply to the onsite test. If the number of students booked for the exam is smaller or equal than 10, the multiple choice exam based on Exam+Respondus can be replaced by an oral exam of approximately 30 minutes, focused on the topics taught both during the lectures and at the laboratories, which takes place on a web platform (such as Skype or Zoom) in the online case, and in the Politecnico di Torino premises in the onsite case.