Random processes and signals

Numerous random phenomena occur in nature, such as fluctuations in temperature or atmospheric pressure. In electronics and telecommunications, the study of random processes is particularly useful in the context of digital communications, where certain signals are impossible to characterize a priori. The exploitation of random processes is also at the root of many approaches to signal processing in a variety of application contexts: speech, audio, biomedical, IoT, radar, navigation, finance, etc., whether to characterize the frequency content of a signal (spectral analysis), or to process or compare signals. More generally, information sources such as sound and images are random and vary over time. Finally, random processes have a direct application in network traffic processing, particularly for analyzing the transfer time and/or processing time of a randomly-sized packet of information, generated at random time intervals (Queue Theory). As a basic theoretical course, the Random Processes course aims to introduce the properties and tools for processing time-varying random phenomena. It is part of the Signal and Image Processing curriculum.

probabilities and basic mathematical knowledge

* Characterization of random processes: - Notion of mean, illustrations of a random process in the discrete case, higher-order probability density, properties of autocorrelation and autocovariance functions, stationarity and ergodicity, discrete Karhunen Loeve transform. * Estimation: - Autocorrelation estimators, maximum likelihood (mv) estimation, least squares estimation. *Markov chains: - Reminders of oriented graph theory, discrete-time Markov chains.

Mathematics and signal processing

1 course and TD support.
Therrien Charles W., Discrete Random Signals and Statistical Signal Processing, Prentice Hall, 1992.