Verfügbarkeit: Adaptive filters

Adaptive filters:

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1. Verfasser:	Sayed, Ali H. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	[Piscataway, NJ u.a.] IEEE Press [u.a.] 2008
Schlagworte:	Filtres adaptatifs Adaptive filters Adaptives Filter
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XXX, 786 S. graph. Darst.
ISBN:	9780470253885

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adam_text	Preface xvii Notation xxv Acknowledgments xxx BACKGROUND MATERIAL A Random Variables 1 A. 1 Variance of a Random Variable 1 A.2 Dependent Random Variables 3 A.3 Complex-Valued Random Variables 4 A.4 Vector-Valued Random Variables 6 A.5 Gaussian Random Vectors 7 В Linear Algebra 12 B.I Hermitian and Positive-Definite Matrices 12 B.2 Range Spaces and Nullspaces of Matrices 14 B.3 Schur Complements 16 B.4 Cholesky Factorization 17 B.5 QR Decomposition 19 B.6 Singular Value Decomposition 20 B.7 Kronecker Products 23 С Complex Gradients 25 C.I Cauchy-Riemann Conditions 25 C.2 Scalar Arguments 26 C.3 Vector Arguments 26 PARTI: OPTIMAL ESTIMATION 1 Scalar-Valued Data 29 1.1 Estimation Without Observations 29 1.2 Estimation Given Dependent Observations 31 vii vl 1.3 Orthogonality Principle 36 contents 14 Gaussian Random Variables 38 2 Vector-Valued Data 42 2.1 Optimal Estimator in the Vector Case 42 2.2 Spherically Invariant Gaussian Variables 46 2.3 Equivalent Optimization Criterion 49 Summary and Notes 51 Problems and Computer Projects 54 PART II: LINEAR ESTIMATION 3 Normal Equations 60 3.1 Mean-Square Error Criterion 61 3.2 Mimmization by Differentiation 63 3.3 Minimization by Completion-of-Squares 63 3.4 Minimization of the Error Covariance Matrix 65 3.5 Optimal Linear Estimator 66 4 Orthogonality Principle 67 4.1 Design Examples 67 4.2 Orthogonality Condition 72 4.3 Existence of Solutions 74 4.4 Nonzero-Mean Variables 76 5 Linear Models 78 5.1 Estimation using Linear Relations 78 5.2 Application: Channel Estimation 80 5.3 Application: Block Data Estimation 81 5.4 Application: Linear Channel Equalization 82 5.5 Application: Multiple-Antenna Receivers 85 6 Constrained Estimation 87 6.1 Minimum-Variance Unbiased Estimation 88 6.2 Example: Mean Estimation 90 6.3 Application: Channel and Noise Estimation 91 6.4 Application: Decision Feedback Equalization 93 6.5 Application: Antenna Beamforming 101 7 Kaiman Filter 104 7.1 Innovations Process 104 7.2 State-Space Model 106 7.3 Recursion for the State Estimator 7.4 Computing the Gain Matrix 7.5 Riccati Recursion 7.6 Covariance Form 7.7 Measurement and Time-Update Form Summary and Notes Problems and Computer Projects 107 ix 108 CONTENTS 109 109 110 111 115 PART III : STOCHASTIC GRADIENT ALGORITHMS 8 Steepest-Descent Technique 139 8.1 Linear Estimation Problem 140 8.2 Steepest-Descent Method 142 8.3 More General Cost Functions 147 9 Transient Behavior 148 9.1 Modes of Convergence 148 9.2 Optimal Step-Size 149 9.3 Weight-Error Vector Convergence 151 9.4 Time Constants 153 9.5 Learning Curve 154 9.6 Contour Curves of the Error Surface 155 9.7 Iteration-Dependent Step-Sizes 157 9.8 Newton s Method 160 10 LMS Algorithm 163 10.1 Motivation 163 10.2 Instantaneous Approximation 165 10.3 Computational Cost 166 10.4 Least-Perturbation Property 167 10.5 Application: Adaptive Channel Estimation 168 10.6 Application: Adaptive Channel Equalization 171 10.7 Application: Decision-Feedback Equalization 172 10.8 Ensemble-Average Learning Curves 174 11 Normalized LMS Algorithm 178 11.1 Instantaneous Approximation 178 11.2 Computational Cost 179 11.3 Power Normalization 180 11.4 Least-Perturbation Property 182 12 Other LMS-Type Algorithms 183 12.1 Non-Blind Algorithms 183 CONTENTS 122 Blind Algorithms 186 12.3 Some Properties 188 13 Affine Projection Algorithm 191 13.1 Instantaneous Approximation 191 13.2 Computational Cost 193 13.3 Least-Perturbation Property 193 13.4 Affine Projection Interpretation 194 14 RLS Algorithm 198 14.1 Instantaneous Approximation 198 14.2 Computational Cost 200 Summary and Notes 202 Problems and Computer Projects 209 PART IV: MEAN-SQUARE PERFORMANCE 15 Energy Conservation 228 15.1 Performance Measure 228 15.2 Stationary Data Model 230 15.3 Energy Conservation Relation 234 15.4 Variance Relation 237 15. A Interpretations of the Energy Relation 239 16 Performance of LMS 244 16.1 Variance Relation 244 16.2 Small Step-Sizes 245 16.3 Separation Principle 245 16.4 White Gaussian Input 246 16.5 Statement of Results 249 16.6 Simulation Results 250 17 Performance of NLMS 252 17.1 Separation Principle 252 17.2 Simulation Results 254 17.A Relating NLMS to LMS 254 18 Performance of Sign-Error LMS 257 18.1 Real-Valued Data 257 18.2 Complex-Valued Data 259 18.3 Simulation Results 260 19 Performance of RLS and Other Filters 262 x CONTENTS 19.1 Performance of RLS 262 19.2 Performance of Other Filters 266 19.3 Performance Table for Small Step-Sizes 269 20 Nonstationary Environments 270 20.1 Motivation 270 20.2 Nonstationary Data Model 271 20.3 Energy Conservation Relation 276 20.4 Variance Relation 277 21 Tracking Performance 280 21.1 Performance of LMS 280 21.2 Performance of NLMS 284 21.3 Performance of Sign-Error LMS 285 21.4 Performance of RLS 287 21.5 Comparison of Tracking Performance 289 21.6 Comparing RLS and LMS 292 21.7 Performance of Other Filters 293 21.8 Performance Table for Small Step-Sizes 295 Summary and Notes 296 Problems and Computer Projects 304 PART V: TRANSIENT PERFORMANCE 22 Weighted Energy Conservation 329 22.1 Data Model 329 22.2 Data-Normalized Adaptive Filters 330 22.3 Weighted Energy Conservation Relation 330 22.4 Weighted Variance Relation 333 23 LMS with Gaussian Regressors 340 23.1 Mean and Variance Relations 340 23.2 Mean Behavior 343 23.3 Mean-Square Behavior 343 23.4 Mean-Square Stability 346 23.5 Steady-State Performance 350 23.6 Small Step-Size Approximations 353 23.A Convergence Time 353 24 LMS with non-Gaussian Regressors 357 24.1 Mean and Variance Relations 357 xil 24.2 Mean-Square Stability and Performance 360 contents 24 3 SmaU Step-Size Approximations 362 24.A Independence and Averaging Analysis 363 25 Data-Normalized Filters 371 25.1 NLMS Filter 371 25.2 Data-Normalized Filters 374 25.A Stability Bound 377 25.B Stability of NLMS 378 Summary and Notes 380 Problems and Computer Projects 388 PART VI: BLOCK ADAPTIVE FILTERS 26 Transform Domain Adaptive Filters 413 26.1 Transform-Domain Filters 413 26.2 DFT-Domain LMS 421 26.3 DCT-Domain LMS 423 26.A DCT-Transformed Regressors 424 27 Efficient Block Convolution 426 27.1 Motivation 426 27.2 Block Data Formulation 428 27.3 Block Convolution 431 28 Block and Subband Adaptive Filters 440 28.1 DFT Block Adaptive Filters 440 28.2 Subband Adaptive Filters 447 28.A Another Constrained DFT Block Filter 453 28.B Overlap-Add Block Adaptive Filters 455 Summary and Notes 465 Problems and Computer Projects 468 PART VII: LEAST-SQUARES METHODS 29 Least-Squares Criterion 476 29.1 Least-Squares Problem 477 29.2 Geometric Argument 478 29.3 Algebraic Arguments 480 29.4 Properties of Least-Squares Solution 482 29.5 Projection Matrices 484 29.6 Weighted Least-Squares 485 χίίί 29.7 Regularized Least-Squares 487 contents 29.8 Weighted Regularized Least-Squares 489 30 Recursive Least-Squares 492 30.1 Motivation 492 30.2 RLS Algorithm 493 30.3 Regularization 495 30.4 Conversion Factor 496 30.5 Time-Update of the Minimum Cost 497 30.6 Exponentially-Weighted RLS Algorithm 498 31 Kalman Filtering and RLS 501 31.1 Equivalence in Linear Estimation 501 31.2 Kalman Filtering and Recursive Least-Squares 502 31. A Extended RLS Algorithms 508 32 Order and Time-Update Relations 515 32.1 Backward Order-Update Relations 515 32.2 Forward Order-Update Relations 525 32.3 Time-Update Relation 529 Summary and Notes 534 Problems and Computer Projects 541 PART VIII: ARRAY ALGORITHMS 33 Norm and Angle Preservation 561 33.1 Some Difficulties 561 33.2 Square-Root Factors 562 33.3 Preservation Properties 564 33.4 Motivation for Array Methods 566 34 Unitary Transformations 571 34.1 Givens Rotations 571 34.2 Householder Transformations 576 35 QR and Inverse QR Algorithms 580 35.1 Inverse QR Algorithm 581 35.2 QR Algorithm 584 35.3 Extended QR Algorithm 588 35.A Array Algorithms for Kalman Filtering 589 Summary and Notes 593 xiv Problems and Computer Projects 595 CONTENTS _____________ __^^^^^^^^__^^^^^__^^^^_^__^^^^^^^^_ PART IX: FAST RLS ALGORITHMS 36 Hyperbolic Rotations 602 36.1 Hyperbolic Givens Rotations 602 36.2 Hyperbolic Householder Transfonnations 605 36.3 Hyperbolic Basis Rotations 608 37 Fast Array Algorithm 610 37.1 Time-Update of the Gain Vector 611 37.2 Time-Update of the Conversion Factor 612 37.3 Initial Conditions 613 37.4 Array Algorithm 614 37. A Chandrasekhar Filter 618 38 Regularized Prediction Problems 621 38.1 Regularized Backward Prediction 622 38.2 Regularized Forward Prediction 624 38.3 Low-Rank Factorization 627 39 Fast Fixed-Order Filters 628 39.1 Fast Transversal Filter 628 39.2 FAEST Filter 630 39.3 Fast Kalman Filter 631 39.4 Stability Issues 633 Summary and Notes 639 Problems and Computer Projects 642 PARTX: LATTICE FILTERS 40 Three Basic Estimation Problems 653 40.1 Motivation for Lattice Filters 654 40.2 Joint Process Estimation 656 40.3 Backward Estimation Problem 659 40.4 Forward Estimation Problem 662 40.5 Time and Order-Update Relations 664 41 Lattice Filter Algorithms 669 41.1 Significance of Data Structure 669 41.2 A Posteriori-Based Lattice Filter 672 41.3 A Priori-Based Lattice Filter 673 CONTENTS 42 Error-Feedback Lattice Filters 676 42.1 A Priori Error-Feedback Lattice Filter 676 42.2 A Posteriori Error-Feedback Lattice Filter 680 42.3 Normalized Lattice Filter 682 43 Array Lattice Filters 688 43.1 Order-Update of Output Estimation Errors 689 43.2 Order-Update of Backward Estimation Errors 690 43.3 Order-Update of Forward Estimation Errors 691 43.4 Significance of Data Structure 693 Summary and Notes 695 Problems and Computer Projects 698 PART XI: ROBUST FILTERS 44 Indefinite Least-Squares 705 44.1 Indefinite Least-Squares Formulation 705 44.2 Recursive Minimization Algorithm 710 44.3 Time-Update of the Minimum Cost 713 44.4 Singular Weighting Matrices 714 44. A Stationary Points 716 44.B Inertia Conditions 716 45 Robust Adaptive Filters 718 45.1 A Posteriori-Based Robust Filters 718 45.2 e-NLMS Algorithm 724 45.3 A Priori-Based Robust Filters 726 45.4 LMS Algorithm 730 45.A П°° Filters 732 46 Robustness Properties 735 46.1 Robustness of LMS 735 46.2 Robustness of e- N LMS 739 46.3 Robustness of RLS 740 Summary and Notes 743 Problems and Computer Projects 747 REFERENCES AND INDICES References 758 Author Index 775 Subject Index 780
adam_txt	Preface xvii Notation xxv Acknowledgments xxx BACKGROUND MATERIAL A Random Variables 1 A. 1 Variance of a Random Variable 1 A.2 Dependent Random Variables 3 A.3 Complex-Valued Random Variables 4 A.4 Vector-Valued Random Variables 6 A.5 Gaussian Random Vectors 7 В Linear Algebra 12 B.I Hermitian and Positive-Definite Matrices 12 B.2 Range Spaces and Nullspaces of Matrices 14 B.3 Schur Complements 16 B.4 Cholesky Factorization 17 B.5 QR Decomposition 19 B.6 Singular Value Decomposition 20 B.7 Kronecker Products 23 С Complex Gradients 25 C.I Cauchy-Riemann Conditions 25 C.2 Scalar Arguments 26 C.3 Vector Arguments 26 PARTI: OPTIMAL ESTIMATION 1 Scalar-Valued Data 29 1.1 Estimation Without Observations 29 1.2 Estimation Given Dependent Observations 31 vii vl" 1.3 Orthogonality Principle 36 contents 14 Gaussian Random Variables 38 2 Vector-Valued Data 42 2.1 Optimal Estimator in the Vector Case 42 2.2 Spherically Invariant Gaussian Variables 46 2.3 Equivalent Optimization Criterion 49 Summary and Notes 51 Problems and Computer Projects 54 PART II: LINEAR ESTIMATION 3 Normal Equations 60 3.1 Mean-Square Error Criterion 61 3.2 Mimmization by Differentiation 63 3.3 Minimization by Completion-of-Squares 63 3.4 Minimization of the Error Covariance Matrix 65 3.5 Optimal Linear Estimator 66 4 Orthogonality Principle 67 4.1 Design Examples 67 4.2 Orthogonality Condition 72 4.3 Existence of Solutions 74 4.4 Nonzero-Mean Variables 76 5 Linear Models 78 5.1 Estimation using Linear Relations 78 5.2 Application: Channel Estimation 80 5.3 Application: Block Data Estimation 81 5.4 Application: Linear Channel Equalization 82 5.5 Application: Multiple-Antenna Receivers 85 6 Constrained Estimation 87 6.1 Minimum-Variance Unbiased Estimation 88 6.2 Example: Mean Estimation 90 6.3 Application: Channel and Noise Estimation 91 6.4 Application: Decision Feedback Equalization 93 6.5 Application: Antenna Beamforming 101 7 Kaiman Filter 104 7.1 Innovations Process 104 7.2 State-Space Model 106 7.3 Recursion for the State Estimator 7.4 Computing the Gain Matrix 7.5 Riccati Recursion 7.6 Covariance Form 7.7 Measurement and Time-Update Form Summary and Notes Problems and Computer Projects 107 ix 108 CONTENTS 109 109 110 111 115 PART III : STOCHASTIC GRADIENT ALGORITHMS 8 Steepest-Descent Technique 139 8.1 Linear Estimation Problem 140 8.2 Steepest-Descent Method 142 8.3 More General Cost Functions 147 9 Transient Behavior 148 9.1 Modes of Convergence 148 9.2 Optimal Step-Size 149 9.3 Weight-Error Vector Convergence 151 9.4 Time Constants 153 9.5 Learning Curve 154 9.6 Contour Curves of the Error Surface 155 9.7 Iteration-Dependent Step-Sizes 157 9.8 Newton's Method 160 10 LMS Algorithm 163 10.1 Motivation 163 10.2 Instantaneous Approximation 165 10.3 Computational Cost 166 10.4 Least-Perturbation Property 167 10.5 Application: Adaptive Channel Estimation 168 10.6 Application: Adaptive Channel Equalization 171 10.7 Application: Decision-Feedback Equalization 172 10.8 Ensemble-Average Learning Curves 174 11 Normalized LMS Algorithm 178 11.1 Instantaneous Approximation 178 11.2 Computational Cost 179 11.3 Power Normalization 180 11.4 Least-Perturbation Property 182 12 Other LMS-Type Algorithms 183 12.1 Non-Blind Algorithms 183 CONTENTS 122 Blind Algorithms 186 12.3 Some Properties 188 13 Affine Projection Algorithm 191 13.1 Instantaneous Approximation 191 13.2 Computational Cost 193 13.3 Least-Perturbation Property 193 13.4 Affine Projection Interpretation 194 14 RLS Algorithm 198 14.1 Instantaneous Approximation 198 14.2 Computational Cost 200 Summary and Notes 202 Problems and Computer Projects 209 PART IV: MEAN-SQUARE PERFORMANCE 15 Energy Conservation 228 15.1 Performance Measure 228 15.2 Stationary Data Model 230 15.3 Energy Conservation Relation 234 15.4 Variance Relation 237 15. A Interpretations of the Energy Relation 239 16 Performance of LMS 244 16.1 Variance Relation 244 16.2 Small Step-Sizes 245 16.3 Separation Principle 245 16.4 White Gaussian Input 246 16.5 Statement of Results 249 16.6 Simulation Results 250 17 Performance of NLMS 252 17.1 Separation Principle 252 17.2 Simulation Results 254 17.A Relating NLMS to LMS 254 18 Performance of Sign-Error LMS 257 18.1 Real-Valued Data 257 18.2 Complex-Valued Data 259 18.3 Simulation Results 260 19 Performance of RLS and Other Filters 262 x' CONTENTS 19.1 Performance of RLS 262 19.2 Performance of Other Filters 266 19.3 Performance Table for Small Step-Sizes 269 20 Nonstationary Environments 270 20.1 Motivation 270 20.2 Nonstationary Data Model 271 20.3 Energy Conservation Relation 276 20.4 Variance Relation 277 21 Tracking Performance 280 21.1 Performance of LMS 280 21.2 Performance of NLMS 284 21.3 Performance of Sign-Error LMS 285 21.4 Performance of RLS 287 21.5 Comparison of Tracking Performance 289 21.6 Comparing RLS and LMS 292 21.7 Performance of Other Filters 293 21.8 Performance Table for Small Step-Sizes 295 Summary and Notes 296 Problems and Computer Projects 304 PART V: TRANSIENT PERFORMANCE 22 Weighted Energy Conservation 329 22.1 Data Model 329 22.2 Data-Normalized Adaptive Filters 330 22.3 Weighted Energy Conservation Relation 330 22.4 Weighted Variance Relation 333 23 LMS with Gaussian Regressors 340 23.1 Mean and Variance Relations 340 23.2 Mean Behavior 343 23.3 Mean-Square Behavior 343 23.4 Mean-Square Stability 346 23.5 Steady-State Performance 350 23.6 Small Step-Size Approximations 353 23.A Convergence Time 353 24 LMS with non-Gaussian Regressors 357 24.1 Mean and Variance Relations 357 xil 24.2 Mean-Square Stability and Performance 360 contents 24 3 SmaU Step-Size Approximations 362 24.A Independence and Averaging Analysis 363 25 Data-Normalized Filters 371 25.1 NLMS Filter 371 25.2 Data-Normalized Filters 374 25.A Stability Bound 377 25.B Stability of NLMS 378 Summary and Notes 380 Problems and Computer Projects 388 PART VI: BLOCK ADAPTIVE FILTERS 26 Transform Domain Adaptive Filters 413 26.1 Transform-Domain Filters 413 26.2 DFT-Domain LMS 421 26.3 DCT-Domain LMS 423 26.A DCT-Transformed Regressors 424 27 Efficient Block Convolution 426 27.1 Motivation 426 27.2 Block Data Formulation 428 27.3 Block Convolution 431 28 Block and Subband Adaptive Filters 440 28.1 DFT Block Adaptive Filters 440 28.2 Subband Adaptive Filters 447 28.A Another Constrained DFT Block Filter 453 28.B Overlap-Add Block Adaptive Filters 455 Summary and Notes 465 Problems and Computer Projects 468 PART VII: LEAST-SQUARES METHODS 29 Least-Squares Criterion 476 29.1 Least-Squares Problem 477 29.2 Geometric Argument 478 29.3 Algebraic Arguments 480 29.4 Properties of Least-Squares Solution 482 29.5 Projection Matrices 484 29.6 Weighted Least-Squares 485 χίίί 29.7 Regularized Least-Squares 487 contents 29.8 Weighted Regularized Least-Squares 489 30 Recursive Least-Squares 492 30.1 Motivation 492 30.2 RLS Algorithm 493 30.3 Regularization 495 30.4 Conversion Factor 496 30.5 Time-Update of the Minimum Cost 497 30.6 Exponentially-Weighted RLS Algorithm 498 31 Kalman Filtering and RLS 501 31.1 Equivalence in Linear Estimation 501 31.2 Kalman Filtering and Recursive Least-Squares 502 31. A Extended RLS Algorithms 508 32 Order and Time-Update Relations 515 32.1 Backward Order-Update Relations 515 32.2 Forward Order-Update Relations 525 32.3 Time-Update Relation 529 Summary and Notes 534 Problems and Computer Projects 541 PART VIII: ARRAY ALGORITHMS 33 Norm and Angle Preservation 561 33.1 Some Difficulties 561 33.2 Square-Root Factors 562 33.3 Preservation Properties 564 33.4 Motivation for Array Methods 566 34 Unitary Transformations 571 34.1 Givens Rotations 571 34.2 Householder Transformations 576 35 QR and Inverse QR Algorithms 580 35.1 Inverse QR Algorithm 581 35.2 QR Algorithm 584 35.3 Extended QR Algorithm 588 35.A Array Algorithms for Kalman Filtering 589 Summary and Notes 593 xiv Problems and Computer Projects 595 CONTENTS _ _^^^^^^^^_^^^^^_^^^^_^_^^^^^^^^_ PART IX: FAST RLS ALGORITHMS 36 Hyperbolic Rotations 602 36.1 Hyperbolic Givens Rotations 602 36.2 Hyperbolic Householder Transfonnations 605 36.3 Hyperbolic Basis Rotations 608 37 Fast Array Algorithm 610 37.1 Time-Update of the Gain Vector 611 37.2 Time-Update of the Conversion Factor 612 37.3 Initial Conditions 613 37.4 Array Algorithm 614 37. A Chandrasekhar Filter 618 38 Regularized Prediction Problems 621 38.1 Regularized Backward Prediction 622 38.2 Regularized Forward Prediction 624 38.3 Low-Rank Factorization 627 39 Fast Fixed-Order Filters 628 39.1 Fast Transversal Filter 628 39.2 FAEST Filter 630 39.3 Fast Kalman Filter 631 39.4 Stability Issues 633 Summary and Notes 639 Problems and Computer Projects 642 PARTX: LATTICE FILTERS 40 Three Basic Estimation Problems 653 40.1 Motivation for Lattice Filters 654 40.2 Joint Process Estimation 656 40.3 Backward Estimation Problem 659 40.4 Forward Estimation Problem 662 40.5 Time and Order-Update Relations 664 41 Lattice Filter Algorithms 669 41.1 Significance of Data Structure 669 41.2 A Posteriori-Based Lattice Filter 672 41.3 A Priori-Based Lattice Filter 673 CONTENTS 42 Error-Feedback Lattice Filters 676 42.1 A Priori Error-Feedback Lattice Filter 676 42.2 A Posteriori Error-Feedback Lattice Filter 680 42.3 Normalized Lattice Filter 682 43 Array Lattice Filters 688 43.1 Order-Update of Output Estimation Errors 689 43.2 Order-Update of Backward Estimation Errors 690 43.3 Order-Update of Forward Estimation Errors 691 43.4 Significance of Data Structure 693 Summary and Notes 695 Problems and Computer Projects 698 PART XI: ROBUST FILTERS 44 Indefinite Least-Squares 705 44.1 Indefinite Least-Squares Formulation 705 44.2 Recursive Minimization Algorithm 710 44.3 Time-Update of the Minimum Cost 713 44.4 Singular Weighting Matrices 714 44. A Stationary Points 716 44.B Inertia Conditions 716 45 Robust Adaptive Filters 718 45.1 A Posteriori-Based Robust Filters 718 45.2 e-NLMS Algorithm 724 45.3 A Priori-Based Robust Filters 726 45.4 LMS Algorithm 730 45.A П°° Filters 732 46 Robustness Properties 735 46.1 Robustness of LMS 735 46.2 Robustness of e- N LMS 739 46.3 Robustness of RLS 740 Summary and Notes 743 Problems and Computer Projects 747 REFERENCES AND INDICES References 758 Author Index 775 Subject Index 780
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owner	DE-703 DE-1050 DE-11 DE-29T DE-83 DE-20
owner_facet	DE-703 DE-1050 DE-11 DE-29T DE-83 DE-20
physical	XXX, 786 S. graph. Darst.
publishDate	2008
publishDateSearch	2008
publishDateSort	2008
publisher	IEEE Press [u.a.]
record_format	marc
spelling	Sayed, Ali H. Verfasser aut Adaptive filters Ali H. Sayed [Piscataway, NJ u.a.] IEEE Press [u.a.] 2008 XXX, 786 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Filtres adaptatifs Adaptive filters Adaptives Filter (DE-588)4141377-5 gnd rswk-swf Adaptives Filter (DE-588)4141377-5 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016391150&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Sayed, Ali H. Adaptive filters Filtres adaptatifs Adaptive filters Adaptives Filter (DE-588)4141377-5 gnd
subject_GND	(DE-588)4141377-5
title	Adaptive filters
title_auth	Adaptive filters
title_exact_search	Adaptive filters
title_exact_search_txtP	Adaptive filters
title_full	Adaptive filters Ali H. Sayed
title_fullStr	Adaptive filters Ali H. Sayed
title_full_unstemmed	Adaptive filters Ali H. Sayed
title_short	Adaptive filters
title_sort	adaptive filters
topic	Filtres adaptatifs Adaptive filters Adaptives Filter (DE-588)4141377-5 gnd
topic_facet	Filtres adaptatifs Adaptive filters Adaptives Filter
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016391150&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT sayedalih adaptivefilters

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