By Topic

Adaptive Filters

Cover Image Copyright Year: 2008
Author(s): Ali H. Sayed
Publisher: 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
      Copyright Year: 2008

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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

      Page(s): xxxi - 11
      Copyright Year: 2008

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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 View full abstract»

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      Linear Algebra

      Page(s): 12 - 24
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      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 View full abstract»

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      Complex Gradients

      Page(s): 25 - 27
      Copyright Year: 2008

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      This chapter contains sections titled:
      Cauchy-Riemann Conditions
      Scalar Arguments
      Vector Arguments View full abstract»

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      ScalarValued Data

      Page(s): 28 - 41
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Estimation Without Observations
      Estimation Given Dependent Observations
      Orthogonality Principle
      Gaussian Random Variables View full abstract»

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      VectorValued Data

      Page(s): 42 - 50
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Optimal Estimator in the Vector Case
      Spherically Invariant Gaussian Variables
      Equivalent Optimization Criterion View full abstract»

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      Summary and Notes

      Page(s): 51 - 53
      Copyright Year: 2008

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      This chapter contains sections titled:
      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 54 - 58
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      This chapter contains sections titled:
      Problems
      Computer Project View full abstract»

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      Normal Equations

      Page(s): 59 - 66
      Copyright Year: 2008

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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 View full abstract»

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      Orthogonality Principle

      Page(s): 67 - 77
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      This chapter contains sections titled:
      Design Examples
      Orthogonality Condition
      Existence of Solutions
      Nonzero-Mea Variables View full abstract»

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      Linear Models

      Page(s): 78 - 86
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Estimation Using Linear Relations
      Application: Channel Estimation
      Application: Block Data Estimation
      Application: Linear Channel Equalization
      Application: Multiple-Antenna Receivers View full abstract»

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      Constrained Estimation

      Page(s): 87 - 103
      Copyright Year: 2008

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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 View full abstract»

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      Kalman Filter

      Page(s): 104 - 110
      Copyright Year: 2008

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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 View full abstract»

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      Summary and Notes

      Page(s): 111 - 114
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      This chapter contains sections titled:
      Summary of Mean Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 115 - 137
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      This chapter contains sections titled:
      Problems
      Computer Projects View full abstract»

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      SteepestDescent Technique

      Page(s): 138 - 147
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Linear Estimation Problem
      Steepest-Descent Method
      More General Cost Functions View full abstract»

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      Transient Behavior

      Page(s): 148 - 162
      Copyright Year: 2008

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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 View full abstract»

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      LMS Algorithm

      Page(s): 163 - 177
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      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 View full abstract»

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      Normalized LMS Algorithm

      Page(s): 178 - 182
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      This chapter contains sections titled:
      Instantaneous Approximation
      Computational Cost
      Power Normalization
      Least-Perturbation Property View full abstract»

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      Other LMSType Algorithms

      Page(s): 183 - 190
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      This chapter contains sections titled:
      Non-Blind Algorithms
      Blind Algorithms
      Some Properties View full abstract»

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      Affine Projection Algorithm

      Page(s): 191 - 197
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Instantaneous Approximation
      Computational Cost
      Least-Perturbation Property
      Affine Projection Interpretation View full abstract»

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      RLS Algorithm

      Page(s): 198 - 201
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      This chapter contains sections titled:
      Instantaneous Approximation
      Computational Cost View full abstract»

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      Summary and Notes

      Page(s): 202 - 208
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      This chapter contains sections titled:
      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 209 - 226
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      This chapter contains sections titled:
      Problems
      Computer Projects View full abstract»

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      Energy Conservation

      Page(s): 227 - 243
      Copyright Year: 2008

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      This chapter contains sections titled:
      Performance Measure
      Stationary Data Model
      Energy Conservation Relation
      Variance Relation
      Appendix: Energy Relation Interpretations View full abstract»

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      Performance of LMS

      Page(s): 244 - 251
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Variance Relation
      Small Step-Sizes
      Separation Principle
      White Gaussian Input
      Statement of Results
      Simulation Results View full abstract»

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      Performance of NLMS

      Page(s): 252 - 256
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Separation Principle
      Simulation Results
      Appendix: Relating NLMS to LMS View full abstract»

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      Performance of SignError LMS

      Page(s): 257 - 261
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Real-Valued Data
      Complex-Valued Data
      Simulation Results View full abstract»

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      Performance of RLS and Other Filters

      Page(s): 262 - 269
      Copyright Year: 2008

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      This chapter contains sections titled:
      Performance of RLS
      Performance of Other Filters
      Performance Table for Small Step-Sizes View full abstract»

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      Nonstationary Environments

      Page(s): 270 - 279
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Motivation
      Nonstationary Data Model
      Energy Conservation Relation
      Variance Relation View full abstract»

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      Tracking Performance

      Page(s): 280 - 295
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      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 View full abstract»

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      Summary and Notes

      Page(s): 296 - 303
      Copyright Year: 2008

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      This chapter contains sections titled:
      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 304 - 327
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      This chapter contains sections titled:
      Problems
      Computer Projects View full abstract»

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      Weighted Energy Conservation

      Page(s): 328 - 339
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Data Model
      Data-Normalized Adaptive Filters
      Weighted Energy Conservation Relation
      Weighted Variance Relation View full abstract»

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      LMS with Gaussian Regressors

      Page(s): 340 - 356
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      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 View full abstract»

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      LMS with nonGaussian Regressors

      Page(s): 357 - 370
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Mean and Variance Relations
      Mean-Square Stability and Performance
      Small Step-Size Approximations
      Appendix: Averaging Analysis View full abstract»

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      Data Normalized Filters

      Page(s): 371 - 379
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      NLMS Filter
      Data-Normalized Filters
      Appendix: Stability Bound
      Appendix: Stability of NLMS View full abstract»

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      Summary and Notes

      Page(s): 380 - 387
      Copyright Year: 2008

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      This chapter contains sections titled:
      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 388 - 411
      Copyright Year: 2008

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      This chapter contains sections titled:
      Problems
      Computer Project View full abstract»

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      Transform Domain Adaptive Filters

      Page(s): 412 - 425
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Transform-Domain Filters
      DFT-Domain LMS
      DCT-Domain LMS
      Appendix: DCT-Transformed Regressors View full abstract»

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      Efficient Block Convolution

      Page(s): 426 - 439
      Copyright Year: 2008

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      This chapter contains sections titled:
      Motivation
      Block Data Formulation
      Block Convolution View full abstract»

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      Block and Subband Adaptive Filters

      Page(s): 440 - 464
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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 View full abstract»

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      Summary and Notes

      Page(s): 465 - 467
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      This chapter contains sections titled:
      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 468 - 474
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      Problems
      Computer Project View full abstract»

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      LeastSquares Criterion

      Page(s): 475 - 491
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      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 View full abstract»

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      Recursive LeastSquares

      Page(s): 492 - 500
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Motivation
      RLS Algorithm
      Regularization
      Conversion Factor
      Time-Update of the Minimum Cost
      Exponentially-Weighted RLS Algorithm View full abstract»

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      Kalman Filtering and RLS

      Page(s): 501 - 514
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Equivalence in Linear Estimation
      Kalman Filtering and Recursive Least-Squares
      Appendix: Extended RLS Algorithms View full abstract»

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      Order and TimeUpdate Relations

      Page(s): 515 - 533
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      This chapter contains sections titled:
      Backward Order-Update Relations
      Forward Order-Update Relations
      Time-Update Relation View full abstract»

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      Summary and Notes

      Page(s): 534 - 540
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      This chapter contains sections titled:
      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 541 - 559
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      Problems
      Computer Projects View full abstract»

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      Norm and Angle Preservation

      Page(s): 560 - 570
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      This chapter contains sections titled:
      Some Difficulties
      Square-Root Factors
      Preservation Properties
      Motivation for Array Methods View full abstract»

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      Unitary Transformations

      Page(s): 571 - 579
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      This chapter contains sections titled:
      Givens Rotations
      Householder Transformations View full abstract»

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      QR and Inverse QR Algorithms

      Page(s): 580 - 592
      Copyright Year: 2008

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      This chapter contains sections titled:
      Inverse QR Algorithm
      QR Algorithm
      Extended QR Algorithm
      Appendix: Array Kalman Filters View full abstract»

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      Summary and Notes

      Page(s): 593 - 594
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      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 595 - 600
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      Problems
      Computer Project View full abstract»

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      Hyperbolic Rotations

      Page(s): 601 - 609
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      This chapter contains sections titled:
      Hyperbolic Givens Rotations
      Hyperbolic Householder Transformations
      Hyperbolic Basis Rotations View full abstract»

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      Fast Array Algorithm

      Page(s): 610 - 620
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Time-Update of the Gain Vector
      Time-Update of the Conversion Factor
      Initial Conditions
      Array Algorithm
      Appendix: Chandrasekhar Filter View full abstract»

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      Regularized Prediction Problems

      Page(s): 621 - 627
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      This chapter contains sections titled:
      Regularized Backward Prediction
      Regularized Forward Prediction
      Low-Rank Factorization View full abstract»

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      Fast FixedOrder Filters

      Page(s): 628 - 638
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      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Fast Transversal Filter
      Faest Filter
      Fast Kalman Filter
      Stability Issues View full abstract»

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      Summary and Notes

      Page(s): 639 - 641
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      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 642 - 651
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      Problems
      Computer Projects View full abstract»

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      Three Basic Estimation Problems

      Page(s): 652 - 668
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Motivation For Lattice Filters
      Joint Process Estimation
      Backward Estimation Problem
      Forward Estimation Problem
      Time and Order-Update Relations View full abstract»

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      Lattice Filter Algorithms

      Page(s): 669 - 675
      Copyright Year: 2008

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      This chapter contains sections titled:
      Significance of Data Structure
      A Posteriori-Based Lattice Filter
      A Priori-Based Lattice Filter View full abstract»

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      ErrorFeedback Lattice Filters

      Page(s): 676 - 687
      Copyright Year: 2008

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      This chapter contains sections titled:
      A Priori Error-Feedback Lattice Filter
      A Posteriori Error-Feedback Lattice Filter
      Normalized Lattice Filter View full abstract»

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      Array Lattice Filters

      Page(s): 688 - 694
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      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 View full abstract»

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      Summary and Notes

      Page(s): 695 - 697
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      This chapter contains sections titled:
      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 698 - 703
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      Problems
      Computer Project View full abstract»

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      Indefinite LeastSquares

      Page(s): 704 - 717
      Copyright Year: 2008

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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 View full abstract»

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      Robust Adaptive Filters

      Page(s): 718 - 734
      Copyright Year: 2008

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      This chapter contains sections titled:
      A Posteriori-Based Robust Filters
      -NLMS Algorithm
      A Priori-Based Robust Filters
      LMS Algorithm
      Filters View full abstract»

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      Robustness Properties

      Page(s): 735 - 742
      Copyright Year: 2008

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled:
      Robustness of LMS
      Robustness of -NLMS
      Robustness of RLS View full abstract»

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      Summary and Notes

      Page(s): 743 - 746
      Copyright Year: 2008

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      This chapter contains sections titled:
      Summary of Main Results
      Bibliographic Notes View full abstract»

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      Problems and Computer Projects

      Page(s): 747 - 756
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      Problems
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      References

      Page(s): 757 - 774
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      Author Index

      Page(s): 775 - 779
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      Subject Index

      Page(s): 780 - 786
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