Table of Contents

CONTENTS
PREFACE
ChApter 1 WAVELET TRANSFORMS IN SIGNAL PROCESSING 1 Introduction 1
1.1 The continuous wAvelet trAnsform 2
1.2 The discrete wAvelet trAnsform 3
1.3
1.4 The heisenberg uncertAinty principle And time-frequency decompositions 5
1.5 Multi-resolution AnAlysis 5

1.6 Some importAnt properties of wAvelets 6

1.6.1 CompAct support 6
RAtionAl coe.cients 6

1.6.2
1.6.3 Symmetry 6
Smoothness 6

1.6.4
1.6.5 Number of vAnishing moments 7

1.6.6 AnAlytic expression 7

1.7 Current fAst WT Algorithms 7

1.7.1 OrthogonAl wAvelets 7

1.7.2 SemiorthogonAl (nonorthogonAl) wAvelets 8

1.7.3 BiorthogonAl wAvelets 8

1.7.4 WAvelet pAckets 9
HArmonic wAvelets 9

1.7.5
Discussion 9

1.8 REFERENCES 10
ChApter 2 SYSTEM MODELLING 12
Introduction 12

2.1
2.2 The underlying principle of Fourier hArmonic AnAlysis 13

2.3 AutocorrelAtionwAveletAlgorithm 14

2.4 VibrAtion model selection with FT And AutocorrelAtion wAvelet Algorithm 16
2.5 Coe.cients estimAtion with leAst-squAres Algorithm 17

Results And discussion 19

2.6
2.7 ConditionmonitoringofbeAring 23

2.8 Concluding remArks 28

REFERENCES 28
ChApter 3 CONDITION MONITORING 30

3.1 WAvelet AnAlysis 30

3.2 FilterdesignAndfAstcontinuouswAveletAlgorithm 32

3.3 SmAll defect detection of beAring 37

3.3.1 Speci.c frequency rAnges monitoring 39

3.3.2 Signi.cAnt And nAturAl frequencies monitoring 39

3.4 Concluding remArks 41
REFERENCES 42

ChApter 4 PROCESS CONTROL 43
Introduction 43

4.1
4.2 VibrAtion And surfAce quAlity 44

4.2.1 TheoreticAl cAlculAtion of surfAce quAlity 44

4.2.2 VibrAtion during mAchining 46

4.3 AdAptive spline wAvelet Algorithm 47

4.3.1 BAttle-LemAri′e wAvelet .lter design 47

4.3.2 ArbitrAry .ne time-scAle representAtion 49

4.3.3 AdAptive frequency resolution decomposition 51

4.4 Methodologyofexperiment 53
Results And discussions 55

4.5
4.5.1 ExperimentAl results 55
Discussions 63

4.5.2
4.6 Concluding remArks 64
REFERENCES 65

ChApter 5 VIBRATION ANALYSIS 67
Introduction 67

5.1
5.2 MAchining process vibrAtion 68

5.3 WAvelet Algorithm with cross-correlAtion 69

5.4 ExperimentAlset-up 71

5.5 ExperimentAl results 73
Discussion 77

5.6
5.7 Concluding remArks 79
REFERENCES 80

ChApter 6 AUDIO CODING 82

Introduction 82

6.1
6.2 DSP ImplAntAtion of lifting wAvelet trAnsform 84

6.3 Embedded coding And error resilience 88

6.4 Results of experiment And simulAtion 91
Conclusions 93

6.5 REFERENCES 94
ChApter 7 IMAGE QUALITY MEASUREMENT 96

Introduction 96

7.1
7.2 WAveletAnAlysisAndtheliftingscheme 98

7.3 ImAge quAlity evAluAtion 102

7.3.1 ImAge noise AnAlysis 104

7.3.2 ImAge shArpness AnAlysis 105

7.3.3 ImAge brightness AnAlysis 106

7.3.4 ImAge contrAst AnAlysis 106

7.3.5 ImAge MTF AnAlysis 107

7.3.6 ImAge quAlity quAnti.cAtion And clAssi.cAtion 107

7.3.7 OptimisAtion of weighting coe.cients 108

7.4 ExperimentAl results And discussions 110
Conclusions 118

7.5 REFERENCES 119
ChApter 8 IMAGE DENOISING 121
Introduction 121

8.1
8.2 FAst lifting wAvelet AnAlysis 123

8.3 Noise reduction with wAvelet thresholding And derivAtive .ltering 127 GenerAl noise reduction 127
8.3.1 Fine noise reduction 128
8.3.2
8.4 ExperimentAl results And discussions 131
Conclusions 135

8.5 REFERENCES 135
ChApter 9 WIRELESS POSITIONING 138
Introduction 138

9.1
9.2 WAvelet notch .lter design 140

9.3 System model And nArrowbAnd interference detection 145

9.4 ExperimentAl results And discussions 147
Conclusions 155

9.5
REFERENCES 155

ChApter 10 POWER LINE COMMUNICATIONS 157
Introduction 157

10.1
10.2 MulticArrier spreAd spectrum system 162

10.3 CArrier frequency error estimAtion And compensAtion 169

10.4 Time-frequency AnAlysis of noise 170

10.5 Noise detection And .ltering 175

10.6 ExperimentAl results And discussions 178
Conclusions 183

10.7 REFERENCES 184