具体描述
基本信息
书名：Wavelets in Engineering Applications
定价：78.00元
作者：罗高涌
出版社：科学出版社
出版日期：2014-06-01
ISBN：9787030410092
字数：
页码：196
版次：1
装帧：平装
开本：16开
商品重量：0.4kg
编辑推荐
内容提要
《Wavelets in Engineering Applications》收集了作者所研究的小波理论在信息技术中的工程应用的十多篇论文的系统化合集。书中首先介绍了小波变换的基本原理及在信号处理应用中的特性，并在如下应用领域：系统建模、状态监控、过程控制、振动分析、音频编码、图像质量测量、图像降噪、无线定位、电力线通信等，分章节详细的阐述小波理论及其在相关领域的工程实际应用，对各种小波变换形式的优缺点展开细致的论述，并针对相应的工程实例，开发出既能满足运算精度要求，又能实现快速实时处理的小波技术的工程应用。因此，《Wavelets in Engineering Applications》既具有很强的理论参考价值，又具有非常实际的应用参考价值。
目录
作者介绍
文摘
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 deposing A signAl or function x(t)in terms of its frequency ponents, however, it is not locAlised in time. This is A disAdvAntAge of Fourier AnAlysis, in which frequency informAtion cAn only be extrActed for the plete 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 +∞ 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, overe 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 ponents 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 plex 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. WT hAve recently AttrActed much Attention in the reseArch munity. And the technique of WT hAs been Applied in such diverse .elds As digitAl municAtions, 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
1 +∞ dAdb
x(t)= WT(b, A)Ψb,A(t) (1.5)
A2
CΨ .∞
One would often require wAvelet Ψ(t) to hAve pAct 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 putAtionAl 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.
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 deposition of A function x(t) As A lineAr binAtion 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 putAtions 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 deposition 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 deposition of the (j .1) th scAling coe.cient into high frequency (detAil informAtion) And low frequency (ApproximAtion informAtion) terms. Thus, the Al-gorithm deposes 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 depositions
WAvelet AnAlysis is essentiAlly time-frequency deposition. 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. The expression is Also cAlled Heisenberg inequAlity.
WAvelets cAnnot overe this limitAtion, Although they AdApt AutomAticAlly to A signAl’s ponents, in thAt they bee 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 depose 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, 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.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. 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.
1.6.1 CompAct support
If the scAling function And wAvelet Are pActly 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 pActly 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 puter 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.
序言
用户评价
这本书的名字，简洁而有力，直接点明了其核心主题——小波变换在工程领域的应用。这个组合让我联想到了那些在浩瀚数据海洋中精准定位关键信息的“侦探”工具。工程，在我的认知里，是一个充满挑战和创新的领域，而小波变换，则像是为工程师们量身定制的“显微镜”和“透镜”，能够帮助他们揭示肉眼难以察觉的细节，分析那些瞬息万变的现象。我非常好奇书中会如何详尽地介绍小波变换的数学原理，但更让我感兴趣的是它如何被巧妙地应用于各种工程学科。比如，在信号处理领域，它或许能实现更高效的滤波和压缩；在图像分析方面，它或许能带来更清晰的诊断图像；甚至在地球物理勘探中，它也可能帮助科学家们更好地理解地下的结构。我期待书中能够提供清晰的图示和生动的解释，让我能够理解那些复杂的概念。这本书，对我来说，是一次深入了解工程领域前沿技术的机会，一次学习如何运用先进数学工具解决实际问题的绝佳途径。它仿佛是一个宝库，里面藏着能够帮助工程师们突破技术瓶颈、实现更高精度和效率的“秘籍”。
评分“Wavelets in Engineering Applications”这个书名，瞬间在我的脑海中勾勒出一幅充满活力的画面：数据如同海浪般涌动，而小波变换则像是能够捕捉并分析这些海浪的关键技术。我对工程领域一直怀有浓厚的兴趣，尤其是那些能够解决实际问题的创新方法。小波变换，这个词汇本身就带着一种数学的优雅和力量，我曾隐约听说过它在信号处理和图像分析中的强大能力。但“Engineering Applications”的后缀，则将这种理论上的魅力延伸到了更广阔的应用场景。我迫不及待地想知道，这本书会展示哪些令人惊叹的工程案例？例如，它是否能帮助我们更精确地监测航空发动机的运行状态，从而预测潜在的故障？它是否能在通信领域实现更可靠的数据传输，即使在信号干扰严重的环境下？或者，它能否在材料科学中帮助我们理解材料在受力过程中的微观形变？这本书，对我来说，不仅仅是一本关于数学工具的书，更是一次深入了解工程领域是如何运用尖端技术解决复杂问题的绝佳机会。我期望它能给我带来新的视角，让我看到工程技术背后更深层的智慧和创造力。
评分当我看到“Wavelets in Engineering Applications”这个书名时，我的思绪立刻被带入了一个充满可能性和挑战的领域。小波变换，这个词语给我一种“分解与重构”的联想，仿佛它能够将一个庞杂的系统拆解成更易于理解的组成部分，然后又能够根据这些部分精确地重建出完整的图像。工程领域，在我看来，就是一个不断追求效率、精度和创新的舞台。因此，我非常好奇这本书会如何阐释小波变换在其中扮演的角色。我想象着，它或许能帮助工程师们更有效地分析结构振动，预测潜在的危险；或许能辅助医疗诊断，通过分析医学影像中的微小异常来早期发现疾病；甚至可能在环境保护领域，用于分析复杂的环境数据，揭示污染的来源和传播规律。这本书，对我而言，不仅是对一种数学工具的介绍，更是一次对工程实践中智慧运用的一次深刻洞察。我期待书中能够提供扎实的理论基础，但更希望它能通过丰富的实际案例，让我亲身感受到小波变换在解决工程难题时的强大威力，以及它如何推动着工程技术的不断进步，为人类社会的发展贡献力量。
评分这本书名让我立刻联想到了一系列充满想象的图像，比如如海浪般涌动的数据流，又或是巧妙地嵌入了微妙细节的工程设计。虽然我尚未翻开这本书，单是“Wavelets in Engineering Applications”这个标题就足以勾起我强烈的阅读欲望。我一直对那些能够揭示隐藏模式、分解复杂信号的数学工具充满好奇。小波变换，这个词本身就带着一种优雅和力量，仿佛能够穿透事物的表象，触及到其最核心的构成。想象一下，在复杂的振动分析中，它如何捕捉那些转瞬即逝的异常；在图像处理领域，它又如何实现精妙的去噪和特征提取。工程应用，这个词汇更是为我打开了一个充满可能性的世界。从航空航天的精密控制到医学影像的精准诊断，再到材料科学的微观结构分析，我都能预见到小波变换在其中扮演的关键角色。我非常期待书中能够展现那些前沿的研究成果，以及那些将理论转化为实际应用的创新案例。这本书，对我而言，不仅仅是一本技术书籍，更像是一扇通往更深层次工程理解的大门，一扇能够帮助我看到事物更细微之处，更全面地把握问题本质的窗户。它似乎预示着一次智识上的旅程，一次对工程世界奥秘的探索，我已迫不及待想要开始这段发现之旅。
评分当我瞥见这本书名时，脑海中涌现的画面并非那些抽象的数学公式，而是那些在现实世界中默默发挥着巨大作用的工程奇迹。小波变换，这个词语对我来说，或许不像“结构力学”或“流体力学”那样直观，但它却暗示着一种更深层次的洞察力。我常常惊叹于工程师们如何能够化繁为简，在错综复杂的系统中找到关键的节点。而“Wavelets in Engineering Applications”这个组合，仿佛就指向了那样一种“化繁为简”的艺术。我好奇书中会如何阐释小波变换在解决实际工程难题中的具体方法，比如它如何帮助监测桥梁的健康状况，如何优化通信信号的传输质量，又或者如何在生物力学研究中捕捉微小的肌肉运动。我期待书中能够提供一系列引人入胜的案例研究，让我能够清晰地看到这些理论工具如何在实际工程场景中大放异彩。这不仅仅是关于理论的知识，更是关于智慧的实践。它让我思考，究竟是什么样的工程挑战，需要如此精妙的数学工具来应对？而这些工具，又如何塑造了我们今天所见证的工程技术进步？这本书，对我来说，是一次了解工程界“幕后英雄”的机会，是一次学习如何用更具穿透力的方式去审视和解决工程问题的宝贵经历。
相关图书
本站所有内容均为互联网搜索引擎提供的公开搜索信息，本站不存储任何数据与内容，任何内容与数据均与本站无关，如有需要请联系相关搜索引擎包括但不限于百度，google,bing,sogou 等
© 2025 book.cndgn.com All Rights Reserved. 新城书站 版权所有