Adaptive Filters

Cover Image Copyright Year: 2008
Author(s): Ali H. Sayed
Book Type: Wiley-IEEE Press
Content Type : Books & eBooks
Topics: Signal Processing & Analysis
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Abstract

Adaptive 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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      Frontmatter

      Page(s): i - xxx
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      This prelims comprise:
      Half Title
      Title
      Copyright
      Dedication
      Contents
      Preface
      Notation
      Symbols
      Acknowledgments View full abstract»

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      Random Variables

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      This chapter contains sections titled:

    • Variance of a Random Variable

    • Dependent Random Variables

    • Complex-Valued Random Variables

    • Vector-Valued Random Variables

    • Gaussian Random Vectors

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    Linear Algebra

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    This chapter contains sections titled:

  • Hermitian and Positive-Definite Matrices

  • Range Spaces and Nullspaces of Matrices

  • Schur Complements

  • Cholesky Factorization

  • QR Decomposition

  • Singular Value Decomposition

  • Kronecker Products

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    Complex Gradients

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    This chapter contains sections titled:

  • Cauchy-Riemann Conditions

  • Scalar Arguments

  • Vector Arguments

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    ScalarValued Data

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    This chapter contains sections titled:

  • Estimation Without Observations

  • Estimation Given Dependent Observations

  • Orthogonality Principle

  • Gaussian Random Variables

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    VectorValued Data

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    This chapter contains sections titled:

  • Optimal Estimator in the Vector Case

  • Spherically Invariant Gaussian Variables

  • Equivalent Optimization Criterion

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    Summary and Notes

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    This chapter contains sections titled:

  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Project

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    Normal Equations

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    This chapter contains sections titled:

  • Mean-Square Error Criterion

  • Minimization by Differentiation

  • Minimization by Completion of Squares

  • Minimization of the Error Covariance Matrix

  • Optimal Linear Estimator

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    Orthogonality Principle

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    This chapter contains sections titled:

  • Design Examples

  • Orthogonality Condition

  • Existence of Solutions

  • Nonzero-Mea Variables

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    Linear Models

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    This chapter contains sections titled:

  • Estimation Using Linear Relations

  • Application: Channel Estimation

  • Application: Block Data Estimation

  • Application: Linear Channel Equalization

  • Application: Multiple-Antenna Receivers

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    Constrained Estimation

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    This chapter contains sections titled:

  • Minimum-Variance Unbiased Estimation

  • Example: Mean Estimation

  • Application: Channel and Noise Estimation

  • Application: Decision Feedback Equalization

  • Application: Antenna Beamforming

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    Kalman Filter

    Adaptive Filters
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    This chapter contains sections titled:

  • Innovations Process

  • State-Space Model

  • Recursion for the State Estimator

  • Computing the Gain Matrix

  • Riccati Recursion

  • Covariance From

  • Measurement and Time-Update Form

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    Summary and Notes

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    This chapter contains sections titled:

  • Summary of Mean Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Projects

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    SteepestDescent Technique

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    This chapter contains sections titled:

  • Linear Estimation Problem

  • Steepest-Descent Method

  • More General Cost Functions

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    Transient Behavior

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    This chapter contains sections titled:

  • Modes of Convergence

  • Optimal Step-Size

  • Weight-Error Vector Convergence

  • Time Constants

  • Learning Curve

  • Contour Curves of the Error Surface

  • Iteration-Dependent Step-Sizes

  • Newton's Method

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    LMS Algorithm

    Adaptive Filters
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    This chapter contains sections titled:

  • Motivation

  • Instantaneous Approximation

  • Computational Cost

  • Least-Perturbation Property

  • Application: Adaptive Channel Estimation

  • Application: Adaptive Channel Equalization

  • Application: Decision-Feedback Equalization

  • Ensemble-Average Learning Curves

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    Normalized LMS Algorithm

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  • Instantaneous Approximation

  • Computational Cost

  • Power Normalization

  • Least-Perturbation Property

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    Other LMSType Algorithms

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    This chapter contains sections titled:

  • Non-Blind Algorithms

  • Blind Algorithms

  • Some Properties

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    Affine Projection Algorithm

    Adaptive Filters
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    This chapter contains sections titled:

  • Instantaneous Approximation

  • Computational Cost

  • Least-Perturbation Property

  • Affine Projection Interpretation

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    RLS Algorithm

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    This chapter contains sections titled:

  • Instantaneous Approximation

  • Computational Cost

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    Summary and Notes

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    This chapter contains sections titled:

  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Projects

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    Energy Conservation

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    This chapter contains sections titled:

  • Performance Measure

  • Stationary Data Model

  • Energy Conservation Relation

  • Variance Relation

  • Appendix: Energy Relation Interpretations

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    Performance of LMS

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    This chapter contains sections titled:

  • Variance Relation

  • Small Step-Sizes

  • Separation Principle

  • White Gaussian Input

  • Statement of Results

  • Simulation Results

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    Performance of NLMS

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    This chapter contains sections titled:

  • Separation Principle

  • Simulation Results

  • Appendix: Relating NLMS to LMS

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    Performance of SignError LMS

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  • Real-Valued Data

  • Complex-Valued Data

  • Simulation Results

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    Performance of RLS and Other Filters

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    This chapter contains sections titled:

  • Performance of RLS

  • Performance of Other Filters

  • Performance Table for Small Step-Sizes

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    Nonstationary Environments

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    This chapter contains sections titled:

  • Motivation

  • Nonstationary Data Model

  • Energy Conservation Relation

  • Variance Relation

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    Tracking Performance

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    This chapter contains sections titled:

  • Performance of LMS

  • Performance of NLMS

  • Performance of Sign-Error LMS

  • Performance of RLS

  • Comparison of Tracking Performance

  • Comparing RLS and LMS

  • Performance of Other Filters

  • Performance Table for Small Step-Sizes

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    Summary and Notes

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    This chapter contains sections titled:

  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Projects

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    Weighted Energy Conservation

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    This chapter contains sections titled:

  • Data Model

  • Data-Normalized Adaptive Filters

  • Weighted Energy Conservation Relation

  • Weighted Variance Relation

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    LMS with Gaussian Regressors

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    This chapter contains sections titled:

  • Mean and Variance Relations

  • Mean Behavior

  • Mean-Square Behavior

  • Mean-Square Stability

  • Steady-State Performance

  • Small Step-Size Approximations

  • Appendix: Convergence Time

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    LMS with nonGaussian Regressors

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    This chapter contains sections titled:

  • Mean and Variance Relations

  • Mean-Square Stability and Performance

  • Small Step-Size Approximations

  • Appendix: Averaging Analysis

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    Data Normalized Filters

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    This chapter contains sections titled:

  • NLMS Filter

  • Data-Normalized Filters

  • Appendix: Stability Bound

  • Appendix: Stability of NLMS

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    Summary and Notes

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    This chapter contains sections titled:

  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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    This chapter contains sections titled:

  • Problems

  • Computer Project

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    Transform Domain Adaptive Filters

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    This chapter contains sections titled:

  • Transform-Domain Filters

  • DFT-Domain LMS

  • DCT-Domain LMS

  • Appendix: DCT-Transformed Regressors

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    Efficient Block Convolution

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    This chapter contains sections titled:

  • Motivation

  • Block Data Formulation

  • Block Convolution

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    Block and Subband Adaptive Filters

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    This chapter contains sections titled:

  • DFT Block Adaptive Filters

  • Subband Adaptive Filters

  • Appendix: Another Constrained Filter

  • Appendix: Overlap-Add Block Adaptive Filters

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    Summary and Notes

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    This chapter contains sections titled:

  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Project

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    LeastSquares Criterion

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    This chapter contains sections titled:

  • Least-Squares Problem

  • Geometric Argument

  • Algebraic Arguments

  • Properties of Least-Squares Solution

  • Projection Matrices

  • Weighted Least-Squares

  • Regularized Least-Squares

  • Weighted Regularized Least-Squares

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    Recursive LeastSquares

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    This chapter contains sections titled:

  • Motivation

  • RLS Algorithm

  • Regularization

  • Conversion Factor

  • Time-Update of the Minimum Cost

  • Exponentially-Weighted RLS Algorithm

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    Kalman Filtering and RLS

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    This chapter contains sections titled:

  • Equivalence in Linear Estimation

  • Kalman Filtering and Recursive Least-Squares

  • Appendix: Extended RLS Algorithms

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    Order and TimeUpdate Relations

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    This chapter contains sections titled:

  • Backward Order-Update Relations

  • Forward Order-Update Relations

  • Time-Update Relation

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    Summary and Notes

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    This chapter contains sections titled:

  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Projects

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    Norm and Angle Preservation

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    This chapter contains sections titled:

  • Some Difficulties

  • Square-Root Factors

  • Preservation Properties

  • Motivation for Array Methods

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    Unitary Transformations

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    This chapter contains sections titled:

  • Givens Rotations

  • Householder Transformations

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    QR and Inverse QR Algorithms

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    This chapter contains sections titled:

  • Inverse QR Algorithm

  • QR Algorithm

  • Extended QR Algorithm

  • Appendix: Array Kalman Filters

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    Summary and Notes

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  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Project

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    Hyperbolic Rotations

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    This chapter contains sections titled:

  • Hyperbolic Givens Rotations

  • Hyperbolic Householder Transformations

  • Hyperbolic Basis Rotations

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    Fast Array Algorithm

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    This chapter contains sections titled:

  • Time-Update of the Gain Vector

  • Time-Update of the Conversion Factor

  • Initial Conditions

  • Array Algorithm

  • Appendix: Chandrasekhar Filter

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    Regularized Prediction Problems

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    This chapter contains sections titled:

  • Regularized Backward Prediction

  • Regularized Forward Prediction

  • Low-Rank Factorization

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    Fast FixedOrder Filters

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    This chapter contains sections titled:

  • Fast Transversal Filter

  • Faest Filter

  • Fast Kalman Filter

  • Stability Issues

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    Summary and Notes

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  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Projects

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    Three Basic Estimation Problems

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    This chapter contains sections titled:

  • Motivation For Lattice Filters

  • Joint Process Estimation

  • Backward Estimation Problem

  • Forward Estimation Problem

  • Time and Order-Update Relations

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    Lattice Filter Algorithms

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    This chapter contains sections titled:

  • Significance of Data Structure

  • A Posteriori-Based Lattice Filter

  • A Priori-Based Lattice Filter

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    ErrorFeedback Lattice Filters

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    This chapter contains sections titled:

  • A Priori Error-Feedback Lattice Filter

  • A Posteriori Error-Feedback Lattice Filter

  • Normalized Lattice Filter

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    Array Lattice Filters

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    This chapter contains sections titled:

  • Order-Update of Output Estimation Errors

  • Order-Update of Backward Estimation Errors

  • Order-Update of Forward Estimation Errors

  • Significance of Data Structure

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    Summary and Notes

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  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Project

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    Indefinite LeastSquares

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    This chapter contains sections titled:

  • Indefinite Least-Squares Formulation

  • Recursive Minimization Algorithm

  • Time-Update of the Minimum Cost

  • Singular Weighting Matrices

  • Appendix: Stationary Points

  • Appendix: Inertia Conditions

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    Robust Adaptive Filters

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    This chapter contains sections titled:

  • A Posteriori-Based Robust Filters

  • ?>-NLMS Algorithm

  • A Priori-Based Robust Filters

  • LMS Algorithm

  • ?> ?> Filters

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    Robustness Properties

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    This chapter contains sections titled:

  • Robustness of LMS

  • Robustness of ?>-NLMS

  • Robustness of RLS

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    Summary and Notes

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    This chapter contains sections titled:

  • Summary of Main Results

  • Bibliographic Notes

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    Problems and Computer Projects

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  • Problems

  • Computer Project

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    References

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    Author Index

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    Page(s): 775 - 779
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    Subject Index

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    Page(s): 780 - 786
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