The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance
The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance
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DOI：
10.1088/0305-4470/37/5/b01
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发表时间：
2004-02
期刊：
影响因子：
--
通讯作者：
J. Kingsbury
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文献类型：
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作者：
J. Kingsbury
这本书提供了连续和离散小波变换的理论和实践的概述。分为七章，前三章的书是介绍性的，描述了各种形式的小波变换和他们的计算，而其余章节致力于应用在流体，工程，医学和杂项领域。每一章都有很好的介绍，并有合适的例子来演示关键概念。在适当的地方还包括插图，从而为文本增加了视觉方面的内容。一个值得注意的特点是，在每章的末尾，都有一个学术文献的进一步资源列表，感兴趣的读者可以参考。第一章纯粹是对文本的介绍。小波变换的处理从第二章开始，定义了什么是小波。本章继续定义连续小波变换及其逆变换，并描述如何将其用于询问信号。然后将连续小波变换与短时傅立叶变换进行比较。能量和功率谱的规模也进行了讨论，并链接到他们的频率对应。最后介绍了二维连续小波变换。连续小波变换是如何使用墨西哥帽和Morlet小波计算的例子提供了整个。第三章介绍了离散小波变换，并在第二章的最后明确了离散小波变换与连续小波变换的区别。在本章的前半部分，对数离散化的小波函数进行了描述，导致二进网格缩放，框架，正交和正交基，尺度函数和多分辨率表示的讨论。介绍了快速小波变换，并以Haar小波为例说明了快速小波变换的计算。本章的后半部分集中讨论了离散小波变换的各种要点，包括用于信号去噪和平滑的系数操作，Daubechies小波的描述，平移不变性和双正交性的性质，二维离散小波变换和小波包。第四章介绍了小波变换在流体力学中的应用。从基于小波的湍流统计测量的定义开始，本文描述了小波阈值在流体流动分析中的应用。本章的其余部分描述了工程流的小波分析，特别是射流，尾流，湍流和相干结构，以及地球物理流，包括大气和海洋过程。第五章介绍了小波方法在机械加工、材料、动力学和信息工程等工程领域的应用。与前几章不同，本章（以及随后的章节）更多地采用了文献综述的形式，描述了其他作者的发现。本章涉及的领域包括：加工过程的监控，旋转机械的监控，动力系统，混沌系统，无损检测，表面表征和数据压缩。第六章继续在这方面的注意力现在转向小波在医学信号的分析。本章的大部分内容是专门用于分析一维信号（心电图，神经波形，声学信号等），尽管有一小部分是关于二维医学图像的分析。书的第七章和最后一章集中在小波在三个看似无关的应用领域的应用：分形，金融和物理学。小波方法在分形中的处理主要集中在随机分形上，其中一小部分是关于多重分形的。对金融的处理涉及其他作者在研究股票价格、商品行为、市场动态和外汇汇率时使用小波。第四章中未涉及的地球物理部分，即地震、测井、地形特征分析和气候资料分析。正文最后列出了只能顺便提及的其他应用领域。不像大多数其他出版物的主题，这本书不对待小波变换在数学上严格的方式，而是旨在解释力学的小波变换的方式是容易理解的。因此，它作为一个很好的概述的主题，而不是作为一个参考文本。保持数学到最低限度，并从文本中省略繁琐和详细的证明，这本书是最适合那些谁是新的小波或谁想要一个直观的理解的主题。这样的受众可能包括工程专业的研究生以及工程和应用科学领域的专业人员和研究人员。
This book provides an overview of the theory and practice of continuous and discrete wavelet transforms. Divided into seven chapters, the first three chapters of the book are introductory, describing the various forms of the wavelet transform and their computation, while the remaining chapters are devoted to applications in fluids, engineering, medicine and miscellaneous areas. Each chapter is well introduced, with suitable examples to demonstrate key concepts. Illustrations are included where appropriate, thus adding a visual dimension to the text. A noteworthy feature is the inclusion, at the end of each chapter, of a list of further resources from the academic literature which the interested reader can consult. The first chapter is purely an introduction to the text. The treatment of wavelet transforms begins in the second chapter, with the definition of what a wavelet is. The chapter continues by defining the continuous wavelet transform and its inverse and a description of how it may be used to interrogate signals. The continuous wavelet transform is then compared to the short-time Fourier transform. Energy and power spectra with respect to scale are also discussed and linked to their frequency counterparts. Towards the end of the chapter, the two-dimensional continuous wavelet transform is introduced. Examples of how the continuous wavelet transform is computed using the Mexican hat and Morlet wavelets are provided throughout. The third chapter introduces the discrete wavelet transform, with its distinction from the discretized continuous wavelet transform having been made clear at the end of the second chapter. In the first half of the chapter, the logarithmic discretization of the wavelet function is described, leading to a discussion of dyadic grid scaling, frames, orthogonal and orthonormal bases, scaling functions and multiresolution representation. The fast wavelet transform is introduced and its computation is illustrated with an example using the Haar wavelet. The second half of the chapter groups together miscellaneous points about the discrete wavelet transform, including coefficient manipulation for signal denoising and smoothing, a description of Daubechies' wavelets, the properties of translation invariance and biorthogonality, the two-dimensional discrete wavelet transforms and wavelet packets. The fourth chapter is dedicated to wavelet transform methods in the author's own specialty, fluid mechanics. Beginning with a definition of wavelet-based statistical measures for turbulence, the text proceeds to describe wavelet thresholding in the analysis of fluid flows. The remainder of the chapter describes wavelet analysis of engineering flows, in particular jets, wakes, turbulence and coherent structures, and geophysical flows, including atmospheric and oceanic processes. The fifth chapter describes the application of wavelet methods in various branches of engineering, including machining, materials, dynamics and information engineering. Unlike previous chapters, this (and subsequent) chapters are styled more as literature reviews that describe the findings of other authors. The areas addressed in this chapter include: the monitoring of machining processes, the monitoring of rotating machinery, dynamical systems, chaotic systems, non-destructive testing, surface characterization and data compression. The sixth chapter continues in this vein with the attention now turned to wavelets in the analysis of medical signals. Most of the chapter is devoted to the analysis of one-dimensional signals (electrocardiogram, neural waveforms, acoustic signals etc.), although there is a small section on the analysis of two-dimensional medical images. The seventh and final chapter of the book focuses on the application of wavelets in three seemingly unrelated application areas: fractals, finance and geophysics. The treatment on wavelet methods in fractals focuses on stochastic fractals with a short section on multifractals. The treatment on finance touches on the use of wavelets by other authors in studying stock prices, commodity behaviour, market dynamics and foreign exchange rates. The treatment on geophysics covers what was omitted from the fourth chapter, namely, seismology, well logging, topographic feature analysis and the analysis of climatic data. The text concludes with an assortment of other application areas which could only be mentioned in passing. Unlike most other publications in the subject, this book does not treat wavelet transforms in a mathematically rigorous manner but rather aims to explain the mechanics of the wavelet transform in a way that is easy to understand. Consequently, it serves as an excellent overview of the subject rather than as a reference text. Keeping the mathematics to a minimum and omitting cumbersome and detailed proofs from the text, the book is best-suited to those who are new to wavelets or who want an intuitive understanding of the subject. Such an audience may include graduate students in engineering and professionals and researchers in engineering and the applied sciences.