## Discrete Stochastic Processes and Optimal FilteringOptimal 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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### Contents

Gaussian Vectors | |

Introduction to Discrete Time Processes | |

The Wiener Filter | |

Algorithm of | |

The Kalman Filter | |

### Other editions - View all

Discrete Stochastic Processes and Optimal Filtering Jean-Claude Bertein,Roger Ceschi Limited preview - 2013 |

Discrete Stochastic Processes and Optimal Filtering Jean-Claude Bertein,Roger Ceschi No preview available - 2007 |

Discrete Stochastic Processes and Optimal Filtering Jean-Claude Bertein,Roger Ceschi No preview available - 2010 |

### Common terms and phrases

admits the density algorithm autocorrelation Borel Borel algebra calculate causal causal filter centered characteristic function coefficients components conditional expectation converges Cov(X,Y covariance function covariance matrix defined definition DEFlNlTlON DEMONSTRATION denoted density fX distribution function eigenvalues equal equation ergodic estimate example Exercise expression family of r.v. Figure Fourier transform Furthermore Gaussian process Gaussian r.v. Gaussian vector given gradient Hilbert space independent r.v. instant integral invertible Kalman filtering L1 dP L2 dP law PX least mean square line graph linear space linearly measurable mapping multivectors notation NOTE observation obtain orthogonal orthogonal matrix probability density process X20 PROPOSITION random variables random vector XT real r.v. real random vector scalar product second order second-order random sequence signal Solution spectral density stationary theorem transfer function variance VarX vector space verify white noise Wiener filter write WSS process zero