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羅高湧 著

出版社： 科学出版社

ISBN：9787030410092

版次：1

商品编码：11494373

包装：平装

开本：16开

出版时间：2014-06-01

用纸：胶版纸

页数：196

正文语种：中文

內容簡介

《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.

1.2 The continuous wAvelet trAnsform
EquAtion (1.3) is the form of continuous wAvelet trAnsform (CWT). To AnAlyse Any .nite energy signAl, the CWT uses the dilAtion And trAnslAtion of A single wAvelet function Ψ(t) cAlled the mother wAvelet. Suppose thAt the wAvelet Ψ sAtis.es the Admissibility condition
II
.2
II
+∞ I Ψ(ω)I CΨ =dω< ∞ (1.4)
ω
.∞
where Ψ.(ω) is the Fourier trAnsform of Ψ(t). Then, the continuous wAvelet trAnsform WT(b, A) is invertible on its rAnge, And An inverse trAnsform is given by the relAtion[3]
1 +∞ dAdb
x(t)= WT(b, A)Ψb,A(t) (1.5)
A2
CΨ .∞
One would often require wAvelet Ψ(t) to hAve compAct support, or At leAst to hAve fAst decAy As t goes to in.nity, And thAt Ψ.(ω) hAs su.cient decAy As ω goes to in.nity. From the Admissibility condition, it cAn be seen thAt Ψ.(0) hAs to be 0, And, in pArticulAr, Ψ hAs to oscillAte. This hAs given Ψ the nAme wAvelet or “smAll wAve”. This shows the time-frequency locAlisAtion of the wAvelets, which is An importAnt feAture thAt is required for All the wAvelet trAnsforms to mAke them useful for AnAlysing non-stAtionAry signAls.
The CWT mAps A signAl of one independent vAriAble t into A function of two independent vAriAbles A,b. It is cAlculAted by continuously shifting A continuously scAlAble function over A signAl And cAlculAting the correlAtion between the two. This provides A nAturAl tool for time-frequency signAl AnAlysis since eAch templAte Ψb,A is predominAntly locAlised in A certAin region of the time-frequency plAne with A centrAl frequency thAt is inversely proportionAl to A. The chAnge of the Amplitude Around A certAin frequency cAn then be observed. WhAt distinguishes it from the WFT is the multiresolution nAture of the AnAlysis.

1.3 The discrete wAvelet trAnsform
From A computAtionAl point of view, CWT is not e.cient. One wAy to solve this problem is to sAmple the continuous wAvelet trAnsform on A two-dimensionAl grid (Aj ,bj,k). This will not prevent the inversion of the discretised wAvelet trAnsform in generAl[4].
In equAtion (1.3), if the dyAdic scAles Aj =2j Are chosen, And if one chooses bj,k = k2j to AdApt to the scAle fActor Aj , it follows thAt
( II. 1 ∞ t . k2j
2
dj,k =WT(k2j , 2j)= I2jI x(t)Ψˉdt = x(t), Ψj,k(t) (1.6) .∞ 2j
where Ψj,k(t)=2.j/2Ψ(2.j t . k).
The trAnsform thAt only uses the dyAdic vAlues of A And b wAs originAlly cAlled the discrete wAvelet trAnsform (DWT). The wAvelet coe.cients dj,k Are considered As A time-frequency mAp of the originAl signAl x(t). Often for the DWT, A set of
{}
bAsis functions Ψj,k(t), (j, k) ∈ Z2(where Z denotes the set of integers) is .rst chosen, And the goAl is then to .nd the decomposition of A function x(t) As A lineAr combinAtion of the given bAsis functions. It should Also be noted thAt Although
{}
Ψj,k(t), (j, k) ∈ Z2is A bAsis, it is not necessArily orthogonAl. Non-orthogonAl bAses give greAter .exibility And more choice thAn orthogonAl bAses. There is A clAss of DWT thAt cAn be implemented using e.cient Algorithms. These types of wAvelet trAnsforms Are AssociAted with mAthemAticAl structures cAlled multi-resolution Ap-proximAtions. These fAst Algorithms use the property thAt the ApproximAtion spAces Are nested And thAt the computAtions At coArser resolutions cAn be bAsed entirely on the ApproximAtions At the previous .nest level.
In terms of the relAtionship between the wAvelet function Ψ(t) And the scAling function φ(t), nAmely
II ∞II
2 f
II II
I φ.(ω)I = I Ψ.(2j ω)I (1.7)
j=.∞
The discrete scAling function corresponding to the discrete wAvelet function is As follows
(
1 t . 2j k
φj,k(t)= √ φ (1.8)
2j 2j
It is used to discretise the signAl; the sAmpled vAlues Are de.ned As the scAling coe.cients cj,k
∞
cj,k = x(t)φˉ j,k(t)dt (1.9)
.∞
Thus, the wAvelet decomposition Algorithm is obtAined
f
cj+1(k)= h(l)cj (2k . l)
l∈Z
f
dj+1(k)= g(l)cj (2k . l) (1.10)
l∈Z

Fig.1.1 Algorithm of fAst multi-resolution wAvelet trAnsform
where the terms g And h Are high-pAss And low-pAss .lters derived from the wAvelet functionΨ(t) And the scAling function φ(t), the coe.cients dj+1(k)And cj+1(k)rep-resent A decomposition of the (j .1) th scAling coe.cient into high frequency (detAil informAtion) And low frequency (ApproximAtion informAtion) terms. Thus, the Al-gorithm decomposes the originAl signAl x(t) into di.erent frequency bAnds in the time domAin. When Applied recursively, the formulA (1.10) de.nes the fAst wAvelet trAnsform. Fig.1.1 shows the corresponding multi-resolution fAst Algorithm, where 2 denotes down-sAmpling.

1.4 The heisenberg uncertAinty principle And time-frequency decompositions
WAvelet AnAlysis is essentiAlly time-frequency decomposition. The underlying prop-erty of wAvelets is thAt they Are well locAlised in both time And frequency. This mAkes it possible to AnAlyse A signAl in both time And frequency with unprecedented eAse And AccurAcy, zooming in on very brief intervAls of A signAl without losing too much informAtion About frequency. It is emphAsised thAt the wAvelets cAn only be well or optimAlly locAlised. This is becAuse the Heisenberg uncertAinty principle still holds, which cAn be expressed As the product of the two “uncertAinties”, or spreAds of possible vAlues Δt(time intervAl) And Δf(frequency intervAl)thAtis AlwAys AtleAst A certAin minimum number[5]. The expression is Also cAlled Heisenberg inequAlity.
WAvelets cAnnot overcome this limitAtion, Although they AdApt AutomAticAlly to A signAl’s components, in thAt they become wider to AnAlyse low frequencies And thinner to AnAlyse high frequencies.

1.5 Multi-resolution AnAlysis
As discussed in the previous section, multi-resolution AnAlysis links wAvelets with the .lters used in signAl processing. In this ApproAch, the wAvelet is upstAged by A new function, the scAling function, which gives A series of pictures of the signAl, eAch At A resolution di.ering by A fActor of two from the previous resolution. Multi-resolution AnAlysis is A powerful tool for studying signAls with feAtures At vArious scAles. In ApplicAtions, the prActicAl implementAtion of this trAnsformAtion is performed by using A bAsic .lter bAnk, in which wAvelets Are incorporAted into A system thAt uses A cAscAde of .lters to decompose A signAl. EAch resolution hAs its own pAir of .lters: A low-pAss .lter AssociAted with the scAling function, giving An overAll picture of the signAl, And A high-pAss .lter AssociAted with the wAvelet, letting through only the high frequencies AssociAted with the vAriAtions, or detAils.
By judiciously choosing the scAling function, which is Also referred to As the fAther wAvelet[6], one cAn mAke customised wAvelets with the desired properties.
And the wAvelets generAted for multi-resolution AnAlysis cAn be orthogonAl or non-orthogonAl. In mAny cAses no explicit expression for the scAling function is AvAilAble. However, there Are fAst Algorithms thAt use the re.nement or dilAtion equAtion As expressed in equAtion (1.10) to evAluAte the scAling function At dyAdic points[7].In mAny ApplicAtions, it mAy not be necessAry to construct the scAling function itself, but to work directly with the AssociAted .lters.

1.6 Some importAnt properties of wAvelets
So fAr, there is no consensus As to how hArd one should work to choose the best wAvelet for A given ApplicAtion, And there Are no .rm guidelines on how to mAke such A choice[5]. In generAl, there Are two kinds of choices to mAke: the system of rep-resentAtion (continuous or discrete, orthogonAl or nonorthogonAl) And the properties of the wAvelets themselves[8].
1.6.1 CompAct support
If the scAling function And wAvelet Are compActly supported, the .lters h And g Are .nite impulse response (FIR) .lters, so thAt the summAtions in the fAst wAvelet trAnsform Are .nite. This obviously is of use in implementAtion. If they Are not compActly supported, A fAst decAy is desirAble so thAt the .lters cAn be ApproximAted reAsonAbly by .nite impulse response .lters.

1.6.2 RAtionAl coe.cients
For computer implementAtions, it is of use if the coe.cients of the .lters h And g Are rAtionAls.

1.6.3 Symmetry
If the scAling function And wAvelet Are symmetric, then the .lters hAve generAlised lineAr phAse. The Absence of this property cAn leAd to phAse distortion. This is importAnt in signAl processing ApplicAtions.

1.6.4 Smoothness
The smoothness of wAvelets is very importAnt in ApplicAtions. A higher degree of smoothness corresponds to better frequency locAlisAtion of the .lters. Smooth bA-sis functions Are desired in numericAl AnAlysis ApplicAtions where derivAtives Are involved. The order of regulArity of A wAvelet is the number of its continuous derivA-tives.

前言/序言

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