Optimum filtering

The aim of this course is to present basic and advanced tools for developing parametric approaches to signal processing. This includes a review of signal modeling and associated parameter estimation techniques, as well as a presentation of Wiener optimal filtering and adaptive filtering of the LMS or RLS type. Kalman filtering is then discussed in the case of linear and non-linear state-space representation. Finally, particle filtering is presented. These approaches can be applied to various applications (speech, mobile communication, radar, GPS, etc.).

signal processing, digital filtering, random processes

Introduction to modeling (Wold decomposition, sum of sinusoids, AR, MA and ARMA models, variants of these models).
Estimation of AR parameters using the Yule-Walker equation. Analysis of this method in the case where the data are disturbed by additive noise.
Wiener filtering
Adaptive filtering: LMS, NLMS, APA, RLS
Kalman filtering including a presentation of the state-space representation of the system.
Particle filtering.

Signal processing

Course and practical support