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罗高涌 著

图书标签:

• 小波分析
• 工程应用
• 信号处理
• 图像处理
• 数值分析
• 数学物理
• 高等教育
• 理工科
• 科学计算
• 数据分析

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出版社： 科学出版社

ISBN：9787030410092

商品编码：29222902907

包装：平装

出版时间：2014-06-01

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

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内容提要

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《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

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作者介绍

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文摘

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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.

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《波的奥秘：现代工程中的应用探索》 序言 在物理世界中，波无处不在，从微观的量子涨落到宏观的宇宙膨胀，它们以各种形式传递着信息与能量。然而，波的形态并非总是规则的正弦波，许多复杂的现实世界现象，其背后的数学描述却远超简单的周期性振动。《波的奥秘：现代工程中的应用探索》正是为了揭示这些隐藏在复杂波形中的精妙规律，并将其转化为强大的工程工具而诞生的。本书并非一本枯燥的数学定理堆砌，而是致力于展现如何运用波的概念，特别是小波（Wavelets）这一强大的数学工具，来解决工程领域中的实际问题，从而突破传统方法的局限，开启更高效、更精准的工程分析与设计之门。 引言：超越傅里叶，拥抱时频分析的革命 自傅里叶分析问世以来，它极大地推动了我们理解和处理信号的进程。通过将任何信号分解为一系列不同频率的正弦波的叠加，傅里叶分析在诸如通信、音频处理和振动分析等领域取得了辉煌的成就。然而，傅里叶分析的根本局限在于它提供的是信号的全局频率信息，而无法揭示信号在不同时间点上的频率变化。换言之，它告诉你一个信号“包含哪些频率”，却无法准确告诉你“在何时何地出现何种频率”。 在许多工程应用中，这种时域信息的丢失是致命的。例如，在分析机械设备的故障时，关键的异常往往只发生在短暂的瞬间，并且伴随着特定的频率特征。传统的傅里叶分析可能会因为这些瞬时信号被平均到整个时间段，而难以被察觉。同样，在图像处理中，边缘、纹理等重要特征都具有时间和空间上的局部性，需要能够同时捕捉这些局部信息的方法。 正是在这样的背景下，小波分析应运而生。与傅里叶分析不同，小波分析使用一组“小波”（wavelets），这些小波具有有限的持续时间和局部化的能量，并且可以通过伸缩（改变尺度）和移动（改变位置）来匹配信号的不同特征。这使得小波分析能够同时提供信号在时间和频率（或尺度）上的信息，实现“时频局部化”分析。这就像是用一个带有放大镜和定位器的显微镜，可以精确地观察信号在特定时间和特定“尺度”上的细节。 《波的奥秘：现代工程中的应用探索》将系统地介绍小波分析的核心概念，包括连续小波变换（CWT）和离散小波变换（DWT），以及各种不同类型的小波基函数（如Haar、Daubechies、Mexican Hat等）的特性及其适用场景。本书将用清晰的语言和直观的图示，帮助读者理解小波变换的数学原理，并通过大量的工程实例，展示这些原理如何转化为解决实际问题的强大工具。 第一部分：小波分析的理论基石 本部分将为读者构建坚实的小波分析理论基础。我们将从以下几个方面展开： 信号的本质与挑战： 深入探讨工程信号的各种特性，包括周期性、非周期性、瞬时性、噪声以及多尺度特性。分析传统信号处理方法（如傅里叶变换）在处理复杂信号时的局限性，为引入小波分析奠定基础。 连续小波变换（CWT）： 详细阐述CWT的数学定义，解释尺度（scale）和位移（translation）的物理意义。通过构造和分析不同小波函数的示例，展示CWT如何捕捉信号在不同尺度和位置上的信息。我们将探讨CWT在信号去噪、特征提取等方面的潜力。 离散小波变换（DWT）： 重点介绍DWT，这是小波分析在实际工程中应用最广泛的形式。我们将深入讲解多分辨率分析（MRA）的概念，以及DWT如何通过一系列的滤波器组（高通滤波器和低通滤波器）将信号分解成不同尺度的近似（低频）和细节（高频）分量。我们将讨论DWT的能量守恒性、正交性以及其在数据压缩和信号重构中的优势。 小波基函数的选择： 介绍不同类型的小波基函数，如Haar小波、Daubechies小波系列（dbN）、Symlets小波、Coiflets小波等。分析它们的数学性质（如消失矩、支撑长度、对称性）和在不同应用中的优缺点，帮助读者根据具体工程问题选择最合适的小波基。 小波包（Wavelet Packets）与最优分解： 进一步拓展小波分析的工具箱，介绍小波包的概念。小波包提供了更灵活的分解方式，允许对信号的细节分量进行进一步的分解，从而获得更精细的时频分辨率。我们将讨论如何通过信息准则（如熵）来选择最优的小波包分解。 第二部分：小波分析在工程领域的实践应用 理论的构建是为了更好地指导实践。本部分将聚焦于小波分析在各个工程领域的具体应用，通过大量案例研究，展现其解决实际问题的能力。 信号去噪与滤波： 噪声是工程测量中不可避免的问题。小波分析凭借其出色的时频局部化能力，能够有效地将信号的有用信息与噪声分离开。我们将介绍基于小波阈值处理的去噪方法，包括硬阈值和软阈值方法，并分析其在去除不同类型噪声（如高斯噪声、脉冲噪声）时的效果。将通过实例展示在传感器数据、音频信号、图像信号等领域的去噪应用。 特征提取与模式识别： 许多工程系统中的异常或关键信息都表现为信号中的局部突变、瞬时峰值或特定频率成分。小波变换能够将这些特征清晰地展现出来。我们将探讨如何利用小波系数的统计特性、能量分布等信息，来提取信号的特征，并将其用于模式识别。应用场景将涵盖机械故障诊断（如轴承、齿轮的早期故障检测）、生物医学信号分析（如心电图、脑电图的异常检测）以及工业过程监控。 数据压缩： 随着数据量的不断增长，高效的数据压缩技术变得至关重要。小波变换在信号和图像压缩方面表现出色，能够以较低的失真获得较高的压缩比。我们将深入研究基于DWT的图像压缩算法（如JPEG 2000），解释其工作原理，并分析其相对于DCT（离散余弦变换）等传统方法的优势。 信号重构与近似： 在许多情况下，我们需要从原始信号的某个近似版本或部分信息中重构出有用的信号。小波分析提供了强大的信号重构工具。我们将讨论如何利用小波系数来近似和重构信号，以及在保持关键信息的同时，减少数据冗余。 时频分析与瞬态现象探测： 对于那些在时间上具有局部性、频率上具有瞬时性的现象，如冲击、瞬态振动、突发性放电等，小波分析是唯一有效的分析工具。我们将展示如何利用小波变换的二维时频图（scalogram），直观地观测信号的瞬态行为，并将其应用于诸如结构健康监测、材料断裂分析等领域。 特定工程领域的深度应用： 机械工程： 机械故障诊断、振动信号分析、材料疲劳寿命预测、非破坏性检测。 土木工程： 结构健康监测、地震信号分析、材料缺陷检测、桥梁健康评估。 电气工程： 电力系统暂态分析、电能质量监测、高压放电检测、传感器信号处理。 航空航天工程： 飞机结构健康监测、飞行器振动分析、材料损伤检测。 医学工程： 生物信号（ECG, EEG, EMG）分析、医学图像处理、无创诊断。 环境工程： 污染物监测、环境信号噪声去除、水质分析。 第三部分：进阶话题与未来展望 本部分将带领读者深入探讨小波分析的更高级主题，并展望其在未来工程发展中的潜在应用。 多维小波分析： 扩展小波分析的应用范围，讨论二维、三维甚至更高维度的小波变换，以及其在图像处理、视频分析、多维数据分析等领域的应用。 自适应小波与优化： 探讨如何根据信号的特性自适应地选择或构造最优的小波基，以及相关的优化算法。 小波与机器学习的结合： 介绍如何将小波分析作为特征提取器，与机器学习算法（如支持向量机、神经网络）相结合，构建更强大、更鲁棒的预测与分类模型。 小波在新型传感器与探测技术中的应用： 展望小波分析在未来新型传感技术、物联网（IoT）数据处理、智能制造等领域的发展潜力。 小波分析的计算效率与并行化： 探讨如何提高小波变换的计算效率，以及其在高性能计算和实时应用中的实现。 结语 《波的奥秘：现代工程中的应用探索》旨在成为一本既具理论深度又不失实践价值的参考书。我们相信，通过深入理解和掌握小波分析这一强大的数学工具，工程师们将能够更有效地应对日益复杂和精密的工程挑战，推动技术进步，并为创造更美好的未来贡献力量。本书的每一章节都力求逻辑清晰，内容详实，并通过丰富的图表和实例，帮助读者将抽象的数学概念转化为解决实际工程问题的具体方法。我们希望本书能激发读者对波的奥秘的探索热情，并将其所学应用于各自的工程实践中。

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这本书简直是我近期在工程领域研究中的一个意外惊喜。我之前接触过一些关于小波变换的零散资料，但总是感觉不成体系，缺乏一个清晰的脉络。而这本《Wavelets in Engineering Applications》恰恰填补了这一空白。它系统地梳理了小波变换的数学基础，并在此基础上，详细阐述了其在各种工程问题中的应用。我对于书中关于模式识别和数据压缩章节的讲解尤为印象深刻。在实际工作中，我们经常需要从大量的数据中提取有用的信息，或者将数据进行高效的压缩以节省存储空间。书中关于小波在这些方面的应用，提供了一些非常实用的算法和技术，这让我对如何更有效地处理工程数据有了全新的认识。而且，书中使用的语言非常严谨，但又不失清晰，即使是对于一些复杂的概念，也能通过清晰的解释和图示来理解。

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这次借到的这本《Wavelets in Engineering Applications》，虽然封面看上去很“硬核”，但实际阅读体验却远超我的预期。我一直对小波变换这种数学工具的应用场景感到好奇，总觉得它比传统的傅里叶变换更加灵活和强大，尤其是在处理非平稳信号方面。这本书恰好就深入浅出地介绍了小波变换的原理，并且非常实在地展示了它在工程领域的多样化应用。例如，书中对振动分析的章节，详细解释了如何利用小波去识别和定位信号中的瞬态特征，这对于故障诊断和结构健康监测来说，无疑是至关重要的。我个人也曾遇到过类似的工程问题，当时苦于没有合适的工具来精确分析，读到这里的时候，我仿佛找到了“救星”。书中大量的图示和公式推导，虽然需要仔细研读，但对于想要真正理解其精髓的读者来说，是不可或缺的。

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这本书的封面设计简洁大方，深蓝色的背景搭配银色的书名，透露出一种严谨而深邃的科技感。我平时对数学理论和工程应用之间的交叉领域就颇感兴趣，所以当我在书店里看到它时，立刻就被吸引了。虽然我还没有深入阅读，但仅仅是翻阅目录，就能感受到其内容的广度和深度。从基础的数学原理，到各种工程领域的具体应用，这本书似乎涵盖了一个相当完整的知识体系。我尤其期待书中关于信号处理和图像分析部分的讲解，因为这些是我工作中最常接触到的领域，我希望这本书能为我提供一些新的视角和更深入的理论支撑。此外，书中的一些案例研究也引起了我的好奇，它们是如何将抽象的数学工具转化为解决实际工程问题的有效手段的，这一点非常吸引我。整体而言，这本书给我一种“干货满满”的预感，相信在未来一段时间里，它将成为我案头的常客。

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当我翻开这本《Wavelets in Engineering Applications》时，立刻被它严谨的学术风格和深厚的工程实践相结合所吸引。我一直认为，纯粹的数学理论固然重要，但如果不能在实际工程中得到应用，它的价值就会大打折扣。而这本书正是做到了这一点。它不仅详细介绍了小波变换的数学原理，更重要的是，它提供了大量不同工程领域中的实际应用案例。我尤其对书中关于故障诊断和信号去噪的章节感到兴奋，这些都是我们在实际工程项目中经常会遇到的挑战。书中提供的解决方案，不仅有理论上的指导，更有具体的算法实现和效果展示，这对于工程师来说，无疑是非常宝贵的参考资料。我迫不及待地想要将书中学到的知识应用到我的项目实践中，相信它会为我带来新的思路和更优的解决方案。

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说实话，我一开始拿到这本书的时候，有点担心它会不会太过于理论化，让我在实际应用中无从下手。但当我真正开始阅读后，这种顾虑完全打消了。这本书的结构安排非常巧妙，它并没有一开始就堆砌大量的数学公式，而是先从工程领域的一些典型问题入手，然后引出小波变换在解决这些问题中的作用。这种“问题导向”的学习方式，让我更容易理解为什么需要小波变换，以及它具体是如何工作的。我特别欣赏书中对于不同工程学科应用的区分，比如在材料科学、机械工程、以及通信系统等领域的案例分析，都非常具体且贴合实际。例如，在材料科学部分，书中探讨了如何利用小波分析材料的微观结构，发现潜在的缺陷，这对我日后的科研工作会有很大的启发。