The course is taught in English.
The first part of the course introduces the main concepts of analysis and processing of random signals. The types of noise that are more frequently observed in physical systems are considered, as long as the main techniques for their characterization, removal, and prediction, such as spectral estimation, time-frequency analysis, and the Kalman filter.

The second part of the course introduces the basic principles of digital video coding: motion compensation and motion estimation, main video formats, video coding standards of the MPEG and H.26x classes, error resilience principles, video streaming systems and peer-to-peer video streaming.

- Knowledge of the main classes of random processes, both stationary and nonstationary
- Knowledge of the main techniques to characterize and estimate the properties of stationary and nonstationary random processes, such as mean, variance, autocorrelation, and power spectral density
- Knowledge of the concept of optimal linear recursive estimator
- Ability to classify random processes with respect to their properties.
- Ability to apply algorithms to estimate the properties of stationary and nonstationary random processes
- Ability to design an optimal linear recursive estimator
- Knowledge of the basic principles of motion compensated video coding
- Knowledge of main video coding standards
- Knowledge of the principles of scalable video coding, multi view video coding, 3D video coding
- Knowledge of the main error resilience techniques
- Knowledge of video streaming system design
The ability to apply the gained knowledge will be verified through lab exercises.

- Complex analysis of functions in one or two variables.
- Probability theory.
- Basic notions of digital signal processing, such as the concept of frequency and frequency analysis, the concept of linear time-invariant system, the knowledge of how to filter a random process.
- Basic notions of information theory (entropy, lossless and lossy encoding, rate-distortion theory).
- Basic notions on predictive coding.

- Introduction to discrete-time random processes (10 hours)
- Nonstationary random processes (8 hours)
- Introduction to estimation theory (8 hours)
- Spectral estimation (8 hours)
- Time-frequency analysis (8 hours)
- Kalman filter (8 hours)
- Motion compensated video coding: motion estimation and block matching (principles and practical algorithms) (6 hours)
- Video coding formats (4 hours)
- Video coding standards: MPEG-1/2, MPEG-4, H.261, H.263 (6 hours)
- The standard H.265/AVC (6 hours)
- Scalable video coding. Introduction, scalability in MPEG-2, H.264/SVC (6 hours)
- Other video coding standards: H.264/MVC (multiview video coding), 3DTV (6 hours)
- Principles of error resilience: layered coding, unequal error protection, multiple description coding, error concealment (8 hours)
- Video streaming systems (4 hours)
- Video streaming over peer-to-peer networks (4 hours)

For the first part of the course, half of the time will be employed to implement and validate the techniques explained during the lectures using the Matlab software. Also during the second part of the course some of the algorithms described during the lectures will be validated during software labs, for a duration of roughly one third of the time.

Reference books for the first part of the course:
[1] A. Papoulis and S. U. Pillai, 'Probability, Random Variables and Stochastic Processes,' McGraw Hill, 2002.
[2] D. G. Manolakis, V. K. Ingle, and S. M. Kogon, 'Statistical and Adaptive Signal Processing: Spectral Estimation, Signal Modeling, Adaptive Filtering and Array Processing,' Artech House, 2005.
[3] A. Gelb, 'Applied Optimal Estimation,' MIT Press, 1974.

The exam, both for the first and the second part of the course, is a written test based on multiple choice questions. A certain number of points is associated to each correct answer, and the final grade is composed of the sum of the points.