Discrete Stochastic Processes and Optimal Filtering

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Optimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which are used in relation to non-stationary signals. Exercises with solutions feature in each chapter to demonstrate the practical application of these ideas using Matlab.

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Jean-Claude Bertein has a Master?s and PhD degree from the University of Paris VI. He was formerly a research engineer at Alcatel and today is Professor in the Department of Mathematics and Physics at the Graduate School of Electrical and Electronic Engineering (ESIEE Paris). Roger Ceschi is an ENSEA engineer and holds a Master?s and PhD degree from the University of Paris XI. He was formerly Director of the ENSEA and today he is Director General of the ESIEE Amiens. He is also the author of a theorem on analytic signals and is Visiting Professor at the BIPT and BIT Universities in China. Table Of Contents Random vectors Gaussian vectors Introduction to discrete time processes Estimation The Wiener filter Adaptive filtering: algorithms for gradients and the LMS The Kalman filter