This title is concerned with the founding principles of optimal filters. It proposes several reminders about both random vectors and Gaussian vectors. The study of discrete time processes makes it possible to tackle digital filtering; a chapter on estimation gives the principle results necessary for the construction of the Wiener filter and of the adaptive filter used in the case of stationary signals. It concludes with an examination of Kalman filtering which extends optimal filtering to the case of non-stationary signals. Exercises with solutions punctuate each chapter and practical...