## Adaptive filter theory"Adaptive Filter Theory" looks at both the mathematical theory behind various linear adaptive filters with finite-duration impulse response (FIR) and the elements of supervised neural networks. Up-to-date and in-depth treatment of adaptive filters develops concepts in a unified and accessible manner. This highly successful book provides comprehensive coverage of adaptive filters in a highly readable and understandable fashion. Includes an extensive use of illustrative examples; and MATLAB experiments, which illustrate the practical realities and intricacies of adaptive filters, the codes for which can be downloaded from the Web. Covers a wide range of topics including Stochastic Processes, Wiener Filters, and Kalman Filters. For those interested in learning about adaptive filters and the theories behind them. |

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### Contents

INTRODUCTION | 1 |

STATIONARY DISCRETETIME STOCHASTIC PROCESSES | 44 |

WIENER FILTER THEORY | 180 |

Copyright | |

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### Common terms and phrases

adaptive beamformer adaptive equalizer adaptive filter adaptive transversal filter assume autocorrelation function autoregressive backward prediction errors backward prediction-error filter beamformer compute convergence correlation matrix corresponding cross-correlation cross-correlation vector data matrix denote desired response d(n deterministic correlation matrix discrete-time stochastic process eigenvalue spread eigenvectors elements FBLP method filter of order follows forward prediction-error filter FTF algorithm gain vector Givens rotation Hence Hermitian impulse response input data inputs u(n inverse Kalman algorithm Kalman filter lattice predictor LMS algorithm minimum mean-squared error noise normal equation operation optimum orthogonal output process u(n recursive recursive LSL algorithm reflection coefficients represents right side sample scalar Section sequence side of Eq signal solution squares stationary steepest-descent algorithm step-size parameter stochastic process substituting Eq systolic array tap inputs tap-input vector tap-weight vector term transfer function unit circle unitary matrix updated vector u(n weight vector weight-error white-noise process Wiener filter z-transform zero mean