Adaptive Filters: Theory and Applications

802 Pages·2013·8.04 MB·English

by  Behrouz Farhang-Boroujeny

ADAPTIVE FILTERS

ADAPTIVE FILTERS
THEORY AND APPLICATIONS
Second Edition
Behrouz Farhang-Boroujeny
UniversityofUtah
USA
A John Wiley & Sons, Ltd., Publication
Thiseditionfirstpublished2013
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Farhang-Boroujeny,B.
Adaptivefilters:theoryandapplications/BehrouzFarhang-Boroujeny.–Secondedition.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-119-97954-8(cloth)
1.Adaptivefilters.2. Adaptivesignalprocessing. I.Title.
TK7872.F5F372013
621.3815(cid:2)324–dc23
2012050968
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:978-1-119-97954-8
Setin10/12TimesbyLaserwordsPrivateLimited,Chennai,India
To Diana for her continuous support, understanding
and love throughout my career

Contents
Preface xvii
Acknowledgments xxi
1 Introduction 1
1.1 Linear Filters 1
1.2 Adaptive Filters 2
1.3 Adaptive Filter Structures 3
1.4 Adaptation Approaches 7
1.4.1 Approach Based on Wiener Filter Theory 7
1.4.2 Method of Least-Squares 8
1.5 Real and Complex Forms of Adaptive Filters 9
1.6 Applications 9
1.6.1 Modeling 9
1.6.2 Inverse Modeling 11
1.6.3 Linear Prediction 15
1.6.4 Interference Cancellation 20
2 Discrete-Time Signals and Systems 28
2.1 Sequences and z-Transform 28
2.2 Parseval’s Relation 32
2.3 System Function 33
2.4 Stochastic Processes 35
2.4.1 Stochastic Averages 35
2.4.2 z-Transform Representations 37
2.4.3 The Power Spectral Density 38
2.4.4 Response of Linear Systems to Stochastic Processes 41
2.4.5 Ergodicity and Time Averages 44
Problems 44
3 Wiener Filters 48
3.1 Mean-Squared Error Criterion 48
3.2 Wiener Filter – Transversal, Real-Valued Case 50
viii Contents
3.3 Principle of Orthogonality 55
3.4 Normalized Performance Function 57
3.5 Extension to Complex-Valued Case 58
3.6 Unconstrained Wiener Filters 61
3.6.1 Performance Function 61
3.6.2 Optimum Transfer Function 64
3.6.3 Modeling 66
3.6.4 Inverse Modeling 69
3.6.5 Noise Cancellation 74
3.7 Summary and Discussion 79
Problems 80
4 Eigenanalysis and Performance Surface 90
4.1 Eigenvalues and Eigenvectors 90
4.2 Properties of Eigenvalues and Eigenvectors 91
4.3 Performance Surface 104
Problems 112
5 Search Methods 119
5.1 Method of Steepest Descent 120
5.2 Learning Curve 126
5.3 Effect of Eigenvalue Spread 130
5.4 Newton’s Method 131
5.5 An Alternative Interpretation of Newton’s Algorithm 133
Problems 135
6 LMS Algorithm 139
6.1 Derivation of LMS Algorithm 139
6.2 Average Tap-Weight Behavior of the LMS Algorithm 141
6.3 MSE Behavior of the LMS Algorithm 144
6.3.1 Learning Curve 146
6.3.2 Weight-Error Correlation Matrix 149
6.3.3 Excess MSE and Misadjustment 151
6.3.4 Stability 153
6.3.5 The Effect of Initial Values of Tap Weights
on the Transient Behavior of the
LMS Algorithm 155
6.4 Computer Simulations 156
6.4.1 System Modeling 156
6.4.2 Channel Equalization 158
6.4.3 Adaptive Line Enhancement 163
6.4.4 Beamforming 165
6.5 Simplified LMS Algorithms 167
6.6 Normalized LMS Algorithm 170
6.7 Affine Projection LMS Algorithm 173
6.8 Variable Step-Size LMS Algorithm 177