Concerned with the founding principles of optimal filters, this volume presents several reminders about both random vectors and Gaussian vectors. The study of discrete time processes allow readers to tackle digital filtering, while 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 examples are given using Matlab software.
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Jean-Claude Bertein is a professor in the mathematics and physics department at the Ecole Supérieure d'Ingénieurs en Electrotechnique et Electronique (ESIEE) in Paris. Roger Ceschi is the director general of the ESIEE in Amiens, France, where he teaches signal theory and the former director general of the ENSEA, a prestigious graduate school of electrical engineering and computer science near Paris.
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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