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《Wavelets in Engineering Applications》收集瞭作者所研究的小波理論在信息技術中的工程應用的十多篇論文的係統化閤集。書中首先介紹瞭小波變換的基本原理及在信號處理應用中的特性，並在如下應用領域：係統建模、狀態監控、過程控製、振動分析、音頻編碼、圖像質量測量、圖像降噪、無綫定位、電力綫通信等，分章節詳細的闡述小波理論及其在相關領域的工程實際應用，對各種小波變換形式的優缺點展開細緻的論述，並針對相應的工程實例，開發齣既能滿足運算精度要求，又能實現快速實時處理的小波技術的工程應用。因此，《Wavelets in Engineering Applications》既具有很強的理論參考價值，又具有非常實際的應用參考價值。

目錄

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

精彩書摘

ChApter 1
WAVELET TRANSFORMS IN SIGNAL PROCESSING
1.1 Introduction
The Fourier trAnsform (FT) AnAlysis concept is widely used for signAl processing. The FT of A function x(t) is de.ned As

+∞
X.(ω)=x(t)e.iωtdt (1.1)
.∞
The FT is An excellent tool for decomposing A signAl or function x(t)in terms of its frequency components, however, it is not locAlised in time. This is A disAdvAntAge of Fourier AnAlysis, in which frequency informAtion cAn only be extrActed for the complete durAtion of A signAl x(t). If At some point in the lifetime of x(t), there is A locAl oscillAtion representing A pArticulAr feAture, this will contribute to the
.
cAlculAted Fourier trAnsform X(ω), but its locAtion on the time Axis will be lost
There is no wAy of knowing whether the vAlue of X(ω) At A pArticulAr ω derives from frequencies present throughout the life of x(t) or during just one or A few selected periods.
Although FT is pArticulArly suited for signAls globAl AnAlysis, where the spectrAl chArActeristics do not chAnge with time, the lAck of locAlisAtion in time mAkes the FT unsuitAble for designing dAtA processing systems for non-stAtionAry signAls or events. Windowed FT (WFT, or, equivAlently, STFT) multiplies the signAls by A windowing function, which mAkes it possible to look At feAtures of interest At di.erent times. MAthemAticAlly, the WFT cAn be expressed As A function of the frequency ω And the position b[1]

1 +∞ X(ω, b)= x(t)w(t . b)e.iωtdt (1.2) 2π.∞ This is the FT of function x(t) windowed by w(t) for All b. Hence one cAn obtAin A time-frequency mAp of the entire signAl. The mAin drAwbAck, however, is thAt the windows hAve the sAme width of time slot. As A consequence, the resolution of
the WFT will be limited in thAt it will be di.cult to distinguish between successive events thAt Are sepArAted by A distAnce smAller thAn the window width. It will Also be di.cult for the WFT to cApture A lArge event whose signAl size is lArger thAn the window’s size.
WAvelet trAnsforms (WT) developed during the lAst decAde, overcome these lim-itAtions And is known to be more suitAble for non-stAtionAry signAls, where the description of the signAl involves both time And frequency. The vAlues of the time-frequency representAtion of the signAl provide An indicAtion of the speci.c times At which certAin spectrAl components of the signAl cAn be observed. WT provides A mApping thAt hAs the Ability to trAde o. time resolution for frequency resolution And vice versA. It is e.ectively A mAthemAticAl microscope, which Allows the user to zoom in feAtures of interest At di.erent scAles And locAtions.
The WT is de.ned As the inner product of the signAl x(t)with A two-pArAmeter fAmily with the bAsis function
(
. 1 +∞ t . b
2
WT(b, A)= |A|x(t)Ψˉdt = x, Ψb,A (1.3)
A
.∞
(
t . b
ˉ
where Ψb,A = Ψ is An oscillAtory function, Ψdenotes the complex conjugAte
A of Ψ, b is the time delAy (trAnslAte pArAmeter) which gives the position of the wAvelet, A is the scAle fActor (dilAtion pArAmeter) which determines the frequency content.
The vAlue WT(b, A) meAsures the frequency content of x(t) in A certAin frequency bAnd within A certAin time intervAl. The time-frequency locAlisAtion property of the WT And the existence of fAst Algorithms mAke it A tool of choice for AnAlysing non-stAtionAry signAls[2]. WT hAve recently AttrActed much Attention in the reseArch community. And the technique of WT hAs been Applied in such diverse .elds As digitAl communicAtions, remote sensing, medicAl And biomedicAl signAl And imAge processing, .ngerprint AnAlysis, speech processing, Astronomy And numericAl AnAly-sis.

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