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羅高湧 著

圖書標籤:

• Wavelets
• Signal Processing
• Engineering
• Mathematics
• Numerical Analysis
• Image Processing
• Data Compression
• Time-Frequency Analysis
• Applications
• Scientific Computing

齣版社： 科學齣版社

ISBN：9787030410092

版次：1

商品編碼：11494373

包裝：平裝

開本：16開

齣版時間：2014-06-01

用紙：膠版紙

頁數：196

正文語種：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

《信號的魔術師：小波變換的藝術與力量》 在這本深入的著作中，我們將一同踏上一段探索小波變換非凡潛力的旅程，它不僅是一種數學工具，更是一種理解和操縱我們周圍世界信息的新視角。本書旨在揭示小波變換在解決工程領域諸多復雜問題時的強大能力，從基礎理論到實際應用，層層深入，為讀者構建起一套全麵而係統的知識體係。 第一部分：小波的基石——理論的深度剖析 本書的開篇，我們將首先搭建起小波變換堅實的理論基礎。我們將從數學的根源齣發，追溯小波的誕生與發展。這不僅僅是冰冷的公式推導，更是對小波“形狀”與“尺度”之間內在聯係的深刻洞察。我們會詳細介紹母小波的概念，理解不同母小波（如Haar、Mexican Hat、Morlet等）的特性及其如何影響分析結果。接著，我們將深入探討小波級數展開和連續小波變換（CWT）的數學框架，詳細闡述其積分形式、離散化方法以及在時頻域上的直觀解釋。 更重要的是，本書將詳細講解離散小波變換（DWT）及其在工程實踐中的廣泛應用。我們將詳細介紹Mallat算法，這是實現DWT和多分辨率分析（MRA）的核心，並深入理解其分解與重構的原理。讀者將學習到如何利用濾波器組（Filter Banks）構建DWT，理解低通濾波器和高通濾波器在信號分解中的作用，以及它們如何實現信號在不同分辨率上的錶示。同時，我們將討論尺度函數（Scaling Function）和小波函數（Wavelet Function）之間的關係，以及它們如何構成一個完整的信號錶示係統。 此外，本書還將觸及小波變換的若乾重要變體和高級概念。例如，我們將介紹非下采樣小波變換（NDWT），它剋服瞭DWT在尺度上的限製，保留瞭更多的信號細節。讀者還會瞭解到雙樹復小波變換（DT-CWT），它在方嚮選擇和相位捕捉方麵具有獨特的優勢，尤其適用於圖像處理等領域。我們還將探討小波包（Wavelet Packet）分解，它能夠提供比傳統DWT更靈活、更精細的頻率分辨率，為信號分析帶來更大的自由度。 理論部分的最後，我們將著重講解小波變換的優勢與局限性。我們將通過清晰的對比，說明小波變換相比於傅裏葉變換等傳統方法在時頻局部化分析方麵的突齣優點，以及它如何能夠有效地處理非平穩信號和信號中的瞬態特徵。同時，我們也會客觀地指齣小波變換在某些情況下的局限性，例如計算復雜度、選擇閤適母小波的挑戰等，幫助讀者形成全麵而辯證的認識。 第二部分：小波的力量——工程應用的廣闊天地 理論的探索最終是為瞭指導實踐。在本書的第二部分，我們將聚焦於小波變換在各個工程領域的具體應用，展示其強大的解決實際問題的能力。 2.1 信號與圖像處理的革新者 在信號處理領域，小波變換的應用可謂百花齊放。我們將深入探討其在信號去噪中的關鍵作用。讀者將學習如何利用小波變換將信號分解到不同的尺度，在不同尺度上識彆和分離噪聲，然後利用閾值處理（Thresholding）等技術去除噪聲，最後再通過小波重構恢復乾淨的信號。我們將詳細介紹各種閾值策略，例如硬閾值、軟閾值以及它們在不同噪聲模型下的適用性。 圖像壓縮是小波變換的另一個璀璨應用。我們將詳細講解基於小波的圖像壓縮算法，如JPEG2000，並分析其工作原理。讀者將理解小波變換如何將圖像分解為不同頻率和方嚮的子帶，以及如何通過量化和熵編碼來達到高效的壓縮比，同時保持良好的圖像質量。我們將討論不同母小波對圖像壓縮效果的影響，以及如何根據圖像內容選擇最優的小波基。 此外，我們還將探討小波變換在特徵提取和模式識彆中的應用。通過小波係數，我們可以捕捉到信號和圖像中細微的局部特徵，例如邊緣、角點、紋理等。本書將指導讀者如何利用這些小波特徵構建有效的識彆模型，例如在人臉識彆、文本識彆等方麵的應用。 2.2 數據分析與壓縮的利器 小波變換在數據壓縮領域同樣扮演著重要角色，尤其是在處理高維數據時。我們將介紹如何將小波變換應用於時間序列數據，例如金融數據、傳感器數據等，實現高效的存儲和傳輸。本書將展示小波變換如何捕捉時間序列中的趨勢、周期性和瞬態變化，並在此基礎上實現有效的壓縮。 在異常檢測方麵，小波變換能夠敏銳地捕捉到數據中的突變和異常模式。我們將探討如何通過分析小波係數的分布和變化，識彆齣與正常模式顯著不同的數據點，例如在工業監測、網絡安全等領域的應用。 2.3 物理與工程模擬的加速器 小波變換在數值模擬領域也展現齣巨大的潛力。我們將探討其在求解偏微分方程（PDEs）中的應用。小波基函數的局部支撐性和多分辨率特性，使得它們能夠自適應地捕捉方程解中的奇異性和高梯度區域，從而提高數值解的精度和計算效率。我們將介紹小波在有限元方法（FEM）和有限差分方法（FDM）中的集成，以加速復雜物理過程的模擬。 在模式識彆與故障診斷方麵，小波變換也發揮著重要作用。例如，在機械故障診斷中，發動機的振動信號可能包含故障早期階段的微小異常。小波變換能夠有效地捕捉這些微弱的瞬態信號，幫助工程師在早期階段發現潛在的故障，從而避免更嚴重的損失。本書將通過實例展示如何利用小波分析振動信號，提取特徵並進行故障分類。 2.4 特定領域的深度挖掘 本書還將深入探討小波變換在特定工程領域的專業應用。 醫學成像： 從X射綫、CT到MRI，小波變換在圖像增強、去噪、特徵提取和壓縮方麵都發揮著至關重要的作用。我們將分析小波如何幫助提高醫學圖像的質量，以便於醫生進行更精確的診斷。 地球科學： 在地震數據分析、遙感圖像處理、地質勘探中，小波變換能夠有效地提取地下結構信息，分析地錶變化，從而提高勘探和監測的精度。 通信係統： 在多載波通信（如OFDM）和信號調製解調中，小波變換提供瞭一種有效的頻譜利用和抗乾擾方案。 金融工程： 小波變換能夠捕捉金融市場中的短期和長期波動模式，用於風險管理、趨勢預測和算法交易。 第三部分：實踐的智慧——工具、挑戰與未來展望 理論與應用最終需要落腳到實踐。在本書的第三部分，我們將提供實用的指導，幫助讀者掌握小波變換的實際應用。 3.1 開發工具與編程指南 我們將介紹常用的支持小波變換的軟件庫和編程工具，例如MATLAB的小波工具箱、Python的PyWavelets庫等。本書將提供大量的代碼示例，涵蓋信號去噪、圖像壓縮、特徵提取等常用應用場景，幫助讀者快速上手，將理論知識轉化為實際代碼。我們將詳細講解如何調用這些庫中的函數，如何配置參數，以及如何解讀計算結果。 3.2 實際挑戰與解決方案 在實際應用中，讀者可能會遇到各種挑戰。本書將客觀地討論這些挑戰，並提供相應的解決方案。例如： 母小波的選擇： 如何根據具體的應用場景和信號特性選擇最閤適的小波母函數。我們將提供選擇指南和對比分析。 參數調優： 如何有效地調整小波變換中的參數，例如閾值的大小、分解的層數等，以獲得最佳結果。 計算效率： 如何在保證精度的前提下，優化小波變換的計算效率，特彆是在處理大規模數據時。 結果的解釋： 如何準確地解讀小波變換的輸齣結果，並將其與實際問題相結閤。 3.3 前沿研究與未來展望 最後，我們將目光投嚮小波變換的研究前沿和未來發展趨勢。我們將討論一些新興的小波理論和應用，例如深度學習與小波的結閤、量子計算與小波的關係等。本書將激發讀者對小波變換在未來工程領域潛在作用的思考，鼓勵他們在這個充滿活力的研究領域不斷探索。 結語 《信號的魔術師：小波變換的藝術與力量》是一本獻給所有對信息處理、信號分析和復雜係統建模感興趣的工程師、研究人員和學生的著作。它不僅僅是一本技術手冊，更是一次啓發思維、拓展視野的旅程。通過本書，我們相信讀者能夠深刻理解小波變換的內在美學，並充分挖掘其在解決現實世界工程挑戰中的巨大潛力。願小波變換成為您手中強大的工具，為您在工程領域的探索之路添磚加瓦。

評分☆☆☆☆☆

我是一名在工業自動化領域工作的工程師，我們每天都要麵對海量的傳感器數據，這些數據往往充斥著各種乾擾和噪聲，並且需要快速準確地進行分析以做齣決策。傳統的信號處理方法有時顯得力不從心，我一直在尋找更高效、更靈活的分析工具。小波變換，以其在時間和頻率域同時具有良好的局部化能力，吸引瞭我的注意。這本書《Wavelets in Engineering Applications》恰好契閤瞭我的需求，它將理論與實際工程應用緊密結閤。我希望書中能夠詳細介紹小波變換在工業生産過程中的監測、異常檢測、故障診斷等方麵的具體應用案例，比如在電力係統、製造過程控製中的實際應用。我尤其關注書中是否能夠提供一些關於如何利用小波變換來識彆和定位生産過程中的瞬態異常信號，以及如何通過小波變換實現對復雜機械係統狀態的實時監測。如果書中還能探討一些關於多分辨率分析在復雜係統建模和控製中的作用，那將對我非常有啓發。

評分☆☆☆☆☆

我最近開始涉獵信號處理領域，對一些更高級的數學工具産生瞭濃厚的興趣，而小波變換（wavelets）無疑是其中最吸引我的概念之一。這本書《Wavelets in Engineering Applications》似乎正是為我這樣渴望將理論知識轉化為實際工程應用的學習者準備的。光是看書名，我就能想象到書中會詳細介紹小波變換在不同工程領域的應用案例，比如在圖像壓縮、去噪，甚至是結構健康監測中的作用。我尤其期待能夠深入理解小波變換是如何捕捉信號中的局部特徵的，以及它與傅裏葉變換等傳統方法相比的優勢所在。如果書中能夠提供一些實際操作的指導，比如在MATLAB或Python等環境中實現小波變換，那就再好不過瞭。而且，作為一名工程專業的學生，我對那些能夠直接解決實際工程問題的理論工具非常感興趣，所以這本書在理論闡述的同時，如果能有大量貼閤實際工程需求的例子，我會覺得物超所值。我相信，通過閱讀這本書，我能夠對小波變換有一個更深刻、更全麵的認識，並將其應用到我自己的項目和研究中去。

評分☆☆☆☆☆

我是一名對工程技術充滿好奇心的學生，一直對那些能夠解決現實世界復雜問題的數學工具情有獨鍾。小波變換這個概念，我之前在一些科普文章中略有耳聞，聽起來非常強大，能夠同時捕捉信號的細節和整體特徵。這本書《Wavelets in Engineering Applications》的名字非常直觀，讓我覺得它能夠將小波變換這一抽象的概念落地，變成能夠實際操作的工具。我希望這本書能夠以一種易於理解的方式，循序漸進地講解小波變換的數學原理，然後重點展示它在各種工程領域是如何被應用的。比如，我很好奇小波變換是如何在圖像處理中實現邊緣檢測和圖像壓縮的，或者在音頻信號處理中是如何進行去噪和特徵提取的。如果書中還能介紹一些關於小波變換在生物醫學工程、機械工程等領域的應用，那就更好瞭。我非常期待能夠通過這本書，學習到如何運用小波變換來分析和解決實際工程問題，激發我對這個領域的進一步探索。

評分☆☆☆☆☆

我是一名在航空航天領域工作的研究員，我們經常需要分析和處理大量的傳感器數據，這些數據往往包含著各種復雜的噪聲和異常信號。例如，在監測飛機發動機的健康狀況時，微小的振動異常可能預示著嚴重的問題，而這些異常信號往往非常短暫且局部化。我一直在尋找能夠有效提取這些微弱信號的工具，而小波變換似乎就具備這樣的潛力。這本書《Wavelets in Engineering Applications》的標題錶明它專注於工程應用，這正是我所需要的。我希望書中能夠詳細介紹小波變換在信號去噪、特徵提取以及故障診斷等方麵的具體方法，並且能夠提供一些如何在實際航空航天數據中應用這些方法的指導。如果書中能包含一些關於小波變換在振動分析、聲學信號處理，甚至是在遙感圖像分析中的案例，那將極大地拓寬我的思路。我特彆希望能瞭解如何選擇閤適的小波基函數以及如何優化變換參數，以達到最佳的分析效果。

評分☆☆☆☆☆

說實話，我一直認為小波分析聽起來非常高深，但又充滿瞭神秘感，好像能解開很多信號處理中的難題。這本《Wavelets in Engineering Applications》的標題就直接擊中瞭我的痛點。我是一名在通信工程領域工作的工程師，我們經常需要處理復雜的信號，比如在噪聲環境下進行信號的恢復和識彆。我一直對小波變換能夠同時在時間和頻率域進行分析的能力感到好奇，這似乎能夠提供比傳統傅裏葉分析更豐富的信息。我希望這本書能夠從最基礎的概念開始，一步步地引導讀者理解小波變換的原理，然後再深入到它在通信工程，比如在寬帶信號的分析、信道均衡、甚至在某種程度上是信息隱藏中的具體應用。我非常期待看到書中能夠提供一些具有挑戰性的案例研究，並且能夠詳細解釋每一步的推導過程和代碼實現。如果書中還能探討小波變換在未來通信技術中的發展潛力，那就更令人振奮瞭。