The course gives the basis for the processing of random signals. The main goal is to describe the signal processing techniques designed to extract information from a finite data set, which can be modelled as sequence of measured (or acquired) samples of a random signal.
The course begins by reviewing the foundations of discrete-time random signals, particularly by discussing the quantities that describe them, such as the autocorrelation function and the power spectrum. Both stationary and nonstationary random signals commonly encountered in nature and in man-made devices are discussed. The main part of the course gives the basis of the theory of parameter estimation in both maximum likelihood and Bayesian sense, considering practical examples (i.e, the time of arrival of a signal embedded in noise, the frequencies of oscillations corrupted by additive noise, denoising of a signal by using a Kalman filter, etc...).
Half of the course takes place in the LAIB laboratories, where students implement and characterize in the Matlab environment the methods discussed during the lectures.

1. Knowledge of the foundations of discrete-time random signals
2. Knowledge of the theory and methods of estimation theory
3. Ability to design estimation algorithms
6. Ability to use the Kalman filter for the estimation of random signals
Judgment and communication skills are strengthened during the laboratories thanks 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.

Review of discrete-time random signals (processes) (0.5CFU)
Foundations of estimation theory (1CFU)
Maximum likelihood methods (2CFU)
Bayesian methods (2CFU)
The Kalman filter (0.5CFU)

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

Steven M. Kay, Fundamentals of Statistical signal processing: Estimation Theory, Prentice Hall,1993

The exam is oral. It consists of a discussion of the Matlab-based experiments done during the practical classes. The student has to prepare a report containing the description of the experiments, including the obtained results. The report will be used during the oral examination to describe in detail a single experiment, chosen by the professor. Therefore it is not necessary to include discussions and comments related to the obtained results in the report, since these aspects will be part of the oral examination. However the student is free to include in the report any material he considers useful for the oral examination.

Possible topics addressed during the oral examination are:
- a description of the considered system (or algorithm) and of its simulation model,
- the theoretical background of the methods used in the Matlab-based experiments,
- a discussion of the main parameters adopted in the experiments,
- a clear presentation and discussion of the obtained results,
- a discussion of the methods used to evaluate the performance of the algorithms,
- a comparison with theoretical results (when applicable)

The oral presentation is evaluated based on its correctness, the level of knowledge that the student has acquired on the topic, the ability to apply the acquired know-how, to clearly communicate the technical material with accurate terms and to correctly analyze, interpret, and comment the obtained results.