## Adaptive FiltersAdaptive filtering is a topic of immense practical and theoretical value, having applications in areas ranging from digital and wireless communications to biomedical systems. This book enables readers to gain a gradual and solid introduction to the subject, its applications to a variety of topical problems, existing limitations, and extensions of current theories. The book consists of eleven parts?each part containing a series of focused lectures and ending with bibliographic comments, problems, and computer projects with MATLAB solutions. |

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### Contents

Complex Gradients | |

ScalarValued Data | |

VectorValued Data | |

Summary and Notes | |

Problems and Computer Projects | |

NORMAL EQUATIONS | |

DataNormalized Filters | |

Summary and Notes | |

Problems and Computer Projects | |

Transform Domain Adaptive Filters | |

Efficient Block Convolution | |

Block and Subband Adaptive Filters | |

LeastSquares Criterion | |

Recursive LeastSquares | |

Orthogonality Principle | |

Linear Models | |

Constrained Estimation | |

LEASTSQUARES METHODS | |

Kalman Filter | |

Summary and Notes | |

LATTICE FILTERS | |

SteepestDescent Technique | |

Transient Behavior | |

LMS Algorithm | |

Normalized LMS Algorithm | |

Other LMSType Algorithms | |

TRANSIENT PERFORMANCE | |

Affine Projection Algorithm | |

RLS Algorithm | |

Problems and Computer Projects | |

MEANSQUARE PERFORMANCE | |

ROBUST FILTERS | |

Performance of NLMS | |

Performance of SignError | |

Performance of RLS and Other Filters | |

Nonstationary Environments | |

Performance of | |

Weighted Energy Conservation | |

LMS with Gaussian Regressors | |

LMS with nonGaussian Regressors | |

Kalman Filtering and | |

Order and TimeUpdate Relations | |

Summary and Notes | |

Problems and Computer Projects | |

Norm and Angle Preservation | |

Unitary Transformations | |

QR and Inverse QR Algorithms | |

Summary and Notes | |

Hyperbolic Rotations | |

Fast Array Algorithm | |

Regularized Prediction Problems | |

Fast FixedOrder Filters | |

Summary and Notes | |

Three Basic Estimation Problems | |

Lattice Filter Algorithms | |

ErrorFeedback Lattice Filters | |

Array Lattice Filters | |

Summary and Notes | |

Indefinite LeastSquares | |

RobustAdaptive Filters | |

Robustness Properties | |

Summary and Notes | |

Author Index | |

### Common terms and phrases

adaptive filters algorithm antenna approximations argument assume assumption beamformer channel chapter coefficients column vector Consider convergence cost function covariance matrix data d(i decision device defined denote derived diagonal ea(i eigenvalues EMSE entries estimation error estimation problem estimation theory Euclidean norm evaluate expression given Hessian matrix implementation independent input iteration Kalman filter learning curve Lemma linear equalizer linear estimator linear least-mean-squares estimator mean-square error mean-square performance minimizing minimum mean-square error NLMS noise norm normal equations notation observations obtained orthogonal output plot positive-definite positive-definite matrix Prob real additions recursion regressors result row vector satisfy scalar sequence Show sign-error LMS signal small step-sizes solution steady-state steepest-descent algorithm steepest-descent method step-size stochastic-gradient algorithms symbols theorem uncorrelated update variance relation Verify weight estimate weight vector weight-error vector zero zero-mean random variable