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Discovering Wavelets
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Book Synopsis Discovering Wavelets by : Edward Aboufadel
Download or read book Discovering Wavelets written by Edward Aboufadel and published by John Wiley & Sons. This book was released on 2011-02-14 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and practical introduction to wavelets With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of linear algebra. The basic concepts of wavelet theory are introduced in the context of an explanation of how the FBI uses wavelets to compress fingerprint images. Wavelet theory is further developed in the setting of function spaces. The book then moves on to present more advanced topics such as filters, multiresolution analysis, Daubechies' wavelets, and further applications. The book concludes with a series of projects and problems that introduce advanced topics and offer starting points for research. Sample projects that demonstrate real wavelet applications include image compression, a wavelet-based search engine, processing with Daubechies' wavelets, and more. Among the special features of Discovering Wavelets are: * Real-life, hands-on examples that involve actual wavelet applications * A companion Web site containing Pixel Images software and Maple files to be used with the projects in the book * Challenging problems that reinforce and expand on the ideas being developed * An appendix containing the linear algebra needed to understand wavelets as presented in the book
Download or read book Wavelets written by Amir-Homayoon Najmi and published by JHU Press. This book was released on 2012-04-15 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduced nearly three decades ago as a variable resolution alternative to the Fourier transform, a wavelet is a short oscillatory waveform for analysis of transients. The discrete wavelet transform has remarkable multi-resolution and energy-compaction properties. Amir-Homayoon Najmi’s introduction to wavelet theory explains this mathematical concept clearly and succinctly. Wavelets are used in processing digital signals and imagery from myriad sources. They form the backbone of the JPEG2000 compression standard, and the Federal Bureau of Investigation uses biorthogonal wavelets to compress and store its vast database of fingerprints. Najmi provides the mathematics that demonstrate how wavelets work, describes how to construct them, and discusses their importance as a tool to investigate and process signals and imagery. He reviews key concepts such as frames, localizing transforms, orthogonal and biorthogonal bases, and multi-resolution. His examples include the Haar, the Shannon, and the Daubechies families of orthogonal and biorthogonal wavelets. Our capacity and need for collecting and transmitting digital data is increasing at an astonishing rate. So too is the importance of wavelets to anyone working with and analyzing digital data. Najmi’s primer will be an indispensable resource for those in computer science, the physical sciences, applied mathematics, and engineering who wish to obtain an in-depth understanding and working knowledge of this fascinating and evolving field.
Book Synopsis Wavelets Made Easy by : Yves Nievergelt
Download or read book Wavelets Made Easy written by Yves Nievergelt and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains the nature and computation of mathematical wavelets, which provide a framework and methods for the analysis and the synthesis of signals, images, and other arrays of data. The material presented here addresses the au dience of engineers, financiers, scientists, and students looking for explanations of wavelets at the undergraduate level. It requires only a working knowledge or memories of a first course in linear algebra and calculus. The first part of the book answers the following two questions: What are wavelets? Wavelets extend Fourier analysis. How are wavelets computed? Fast transforms compute them. To show the practical significance of wavelets, the book also provides transitions into several applications: analysis (detection of crashes, edges, or other events), compression (reduction of storage), smoothing (attenuation of noise), and syn thesis (reconstruction after compression or other modification). Such applications include one-dimensional signals (sounds or other time-series), two-dimensional arrays (pictures or maps), and three-dimensional data (spatial diffusion). The ap plications demonstrated here do not constitute recipes for real implementations, but aim only at clarifying and strengthening the understanding of the mathematics of wavelets.
Book Synopsis Conceptual Wavelets in Digital Signal Processing by : D. Lee Fugal
Download or read book Conceptual Wavelets in Digital Signal Processing written by D. Lee Fugal and published by . This book was released on 2009 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A First Course on Wavelets by : Eugenio Hernandez
Download or read book A First Course on Wavelets written by Eugenio Hernandez and published by CRC Press. This book was released on 1996-09-12 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet theory had its origin in quantum field theory, signal analysis, and function space theory. In these areas wavelet-like algorithms replace the classical Fourier-type expansion of a function. This unique new book is an excellent introduction to the basic properties of wavelets, from background math to powerful applications. The authors provide elementary methods for constructing wavelets, and illustrate several new classes of wavelets. The text begins with a description of local sine and cosine bases that have been shown to be very effective in applications. Very little mathematical background is needed to follow this material. A complete treatment of band-limited wavelets follows. These are characterized by some elementary equations, allowing the authors to introduce many new wavelets. Next, the idea of multiresolution analysis (MRA) is developed, and the authors include simplified presentations of previous studies, particularly for compactly supported wavelets. Some of the topics treated include: Several bases generated by a single function via translations and dilations Multiresolution analysis, compactly supported wavelets, and spline wavelets Band-limited wavelets Unconditionality of wavelet bases Characterizations of many of the principal objects in the theory of wavelets, such as low-pass filters and scaling functions The authors also present the basic philosophy that all orthonormal wavelets are completely characterized by two simple equations, and that most properties and constructions of wavelets can be developed using these two equations. Material related to applications is provided, and constructions of splines wavelets are presented. Mathematicians, engineers, physicists, and anyone with a mathematical background will find this to be an important text for furthering their studies on wavelets.
Book Synopsis Ten Lectures on Wavelets by : Ingrid Daubechies
Download or read book Ten Lectures on Wavelets written by Ingrid Daubechies and published by SIAM. This book was released on 1992-01-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of data--such as fingerprints, weather satellite photographs, and medical x-rays--that were previously thought to be impossible to condense without losing crucial details. This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.
Book Synopsis Essential Wavelets for Statistical Applications and Data Analysis by : Todd Ogden
Download or read book Essential Wavelets for Statistical Applications and Data Analysis written by Todd Ogden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: I once heard the book by Meyer (1993) described as a "vulgarization" of wavelets. While this is true in one sense of the word, that of making a sub ject popular (Meyer's book is one of the early works written with the non specialist in mind), the implication seems to be that such an attempt some how cheapens or coarsens the subject. I have to disagree that popularity goes hand-in-hand with debasement. is certainly a beautiful theory underlying wavelet analysis, there is While there plenty of beauty left over for the applications of wavelet methods. This book is also written for the non-specialist, and therefore its main thrust is toward wavelet applications. Enough theory is given to help the reader gain a basic understanding of how wavelets work in practice, but much of the theory can be presented using only a basic level of mathematics. Only one theorem is for mally stated in this book, with only one proof. And these are only included to introduce some key concepts in a natural way.
Book Synopsis A Friendly Guide to Wavelets by : Gerald Kaiser
Download or read book A Friendly Guide to Wavelets written by Gerald Kaiser and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption.
Download or read book Wavelet Theory written by David K. Ruch and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, elementary introduction to wavelet theory and applications Exploring the growing relevance of wavelets in the field of mathematics, Wavelet Theory: An Elementary Approach with Applications provides an introduction to the topic, detailing the fundamental concepts and presenting its major impacts in the world beyond academia. Drawing on concepts from calculus and linear algebra, this book helps readers sharpen their mathematical proof writing and reading skills through interesting, real-world applications. The book begins with a brief introduction to the fundamentals of complex numbers and the space of square-integrable functions. Next, Fourier series and the Fourier transform are presented as tools for understanding wavelet analysis and the study of wavelets in the transform domain. Subsequent chapters provide a comprehensive treatment of various types of wavelets and their related concepts, such as Haar spaces, multiresolution analysis, Daubechies wavelets, and biorthogonal wavelets. In addition, the authors include two chapters that carefully detail the transition from wavelet theory to the discrete wavelet transformations. To illustrate the relevance of wavelet theory in the digital age, the book includes two in-depth sections on current applications: the FBI Wavelet Scalar Quantization Standard and image segmentation. In order to facilitate mastery of the content, the book features more than 400 exercises that range from theoretical to computational in nature and are structured in a multi-part format in order to assist readers with the correct proof or solution. These problems provide an opportunity for readers to further investigate various applications of wavelets. All problems are compatible with software packages and computer labs that are available on the book's related Web site, allowing readers to perform various imaging/audio tasks, explore computer wavelet transformations and their inverses, and visualize the applications discussed throughout the book. Requiring only a prerequisite knowledge of linear algebra and calculus, Wavelet Theory is an excellent book for courses in mathematics, engineering, and physics at the upper-undergraduate level. It is also a valuable resource for mathematicians, engineers, and scientists who wish to learn about wavelet theory on an elementary level.
Book Synopsis Wavelets and Statistics by : Anestis Antoniadis
Download or read book Wavelets and Statistics written by Anestis Antoniadis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its short history, wavelet theory has found applications in a remarkable diversity of disciplines: mathematics, physics, numerical analysis, signal processing, probability theory and statistics. The abundance of intriguing and useful features enjoyed by wavelet and wavelet packed transforms has led to their application to a wide range of statistical and signal processing problems. On November 16-18, 1994, a conference on Wavelets and Statistics was held at Villard de Lans, France, organized by the Institute IMAG-LMC, Grenoble, France. The meeting was the 15th in the series of the Rencontres Pranco-Belges des 8tatisticiens and was attended by 74 mathematicians from 12 different countries. Following tradition, both theoretical statistical results and practical contributions of this active field of statistical research were presented. The editors and the local organizers hope that this volume reflects the broad spectrum of the conference. as it includes 21 articles contributed by specialists in various areas in this field. The material compiled is fairly wide in scope and ranges from the development of new tools for non parametric curve estimation to applied problems, such as detection of transients in signal processing and image segmentation. The articles are arranged in alphabetical order by author rather than subject matter. However, to help the reader, a subjective classification of the articles is provided at the end of the book. Several articles of this volume are directly or indirectly concerned with several as pects of wavelet-based function estimation and signal denoising.
Book Synopsis Introduction to Wavelets and Wavelet Transforms by : C. S. Burrus
Download or read book Introduction to Wavelets and Wavelet Transforms written by C. S. Burrus and published by Pearson. This book was released on 1998 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced undergraduate and beginning graduate students, faculty, researchers and practitioners in signal processing, telecommunications, and computer science, and applied mathematics. It assumes a background of Fourier series and transforms and of linear algebra and matrix methods. This primer presents a well balanced blend of the mathematical theory underlying wavelet techniques and a discussion that gives insight into why wavelets are successful in signal analysis, compression, dection, numerical analysis, and a wide variety of other theoretical and practical applications. It fills a gap in the existing wavelet literature with its unified view of expansions of signals into bases and frames, as well as the use of filter banks as descriptions and algorithms.
Download or read book Wavelets written by John J. Benedetto and published by CRC Press. This book was released on 2021-07-28 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.
Book Synopsis Computational Signal Processing with Wavelets by : Anthony Teolis
Download or read book Computational Signal Processing with Wavelets written by Anthony Teolis and published by Birkhäuser. This book was released on 2017-10-02 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique resource examines the conceptual, computational, and practical aspects of applied signal processing using wavelets. With this book, readers will understand and be able to use the power and utility of new wavelet methods in science and engineering problems and analysis. The text is written in a clear, accessible style avoiding unnecessary abstractions and details. From a computational perspective, wavelet signal processing algorithms are presented and applied to signal compression, noise suppression, and signal identification. Numerical illustrations of these computational techniques are further provided with interactive software (MATLAB code) that is available on the World Wide Web. Topics and Features Continuous wavelet and Gabor transforms Frame-based theory of discretization and reconstruction of analog signals is developed New and efficient "overcomplete" wavelet transform is introduced and applied Numerical illustrations with an object-oriented computational perspective using the Wavelet Signal Processing Workstation (MATLAB code) available This book is an excellent resource for information and computational tools needed to use wavelets in many types of signal processing problems. Graduates, professionals, and practitioners in engineering, computer science, geophysics, and applied mathematics will benefit from using the book and software tools. The present, softcover reprint is designed to make this classic textbook available to a wider audience. A self-contained text that is theoretically rigorous while maintaining contact with interesting applications. A particularly noteworthy topic...is a class of ‘overcomplete wavelets’. These functions are not orthonormal and they lead to many useful results. —Journal of Mathematical Psychology
Book Synopsis Wavelets Through a Looking Glass by : Ola Bratteli
Download or read book Wavelets Through a Looking Glass written by Ola Bratteli and published by Birkhäuser. This book was released on 2013-11-29 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: ? Concise background material for each chapter, open problems, exercises, bibliography, and comprehensive index make this work a fine pedagogical and reference resource.; New previously unpublished results appear on the homotopy of multiresolutions, approximation theory, the spectrum and structure of the fixed points of the associated transfer, subdivision operators; Key topics of wavelet theory are examined; Excellent graphics show how wavelets depend on the spectra of the transfer operators; The important role of the spectrum of a transfer operator is studied; This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory.
Book Synopsis An Introduction to Wavelets by : Charles K. Chui
Download or read book An Introduction to Wavelets written by Charles K. Chui and published by Elsevier. This book was released on 2016-06-03 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet Analysis and its Applications, Volume 1: An Introduction to Wavelets provides an introductory treatise on wavelet analysis with an emphasis on spline-wavelets and time-frequency analysis. This book is divided into seven chapters. Chapter 1 presents a brief overview of the subject, including classification of wavelets, integral wavelet transform for time-frequency analysis, multi-resolution analysis highlighting the important properties of splines, and wavelet algorithms for decomposition and reconstruction of functions. The preliminary material on Fourier analysis and signal theory is covered in Chapters 2 and 3. Chapter 4 covers the introductory study of cardinal splines, while Chapter 5 describes a general approach to the analysis and construction of scaling functions and wavelets. Spline-wavelets are deliberated in Chapter 6. The last chapter is devoted to an investigation of orthogonal wavelets and wavelet packets. This volume serves as a textbook for an introductory one-semester course on “wavelet analysis for upper-division undergraduate or beginning graduate mathematics and engineering students.
Book Synopsis Wavelet Theory by : Somayeh Mohammady
Download or read book Wavelet Theory written by Somayeh Mohammady and published by BoD – Books on Demand. This book was released on 2021-02-24 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior.
Book Synopsis Wavelet and Wave Analysis as Applied to Materials with Micro Or Nanostructure by : Carlo Cattani
Download or read book Wavelet and Wave Analysis as Applied to Materials with Micro Or Nanostructure written by Carlo Cattani and published by World Scientific. This book was released on 2007 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This seminal book unites three different areas of modern science: the micromechanics and nanomechanics of composite materials; wavelet analysis as applied to physical problems; and the propagation of a new type of solitary wave in composite materials, nonlinear waves. Each of the three areas is described in a simple and understandable form, focusing on the many perspectives of the links among the three. All of the techniques and procedures are described here in the clearest and most open form, enabling the reader to quickly learn and use them when faced with the new and more advanced problems that are proposed in this book. By combining these new scientific concepts into a unitary model and enlightening readers on this pioneering field of research, readers will hopefully be inspired to explore the more advanced aspects of this promising scientific direction. The application of wavelet analysis to nanomaterials and waves in nanocomposites can be very appealing to both specialists working on theoretical developments in wavelets as well as specialists applying these methods and experiments in the mechanics of materials. Sample Chapter(s). Chapter 1: Introduction (121 KB). Contents: Wavelet Analysis; Materials with Micro- or Nanostructure; Waves in Materials; Simple and Solitary Waves in Materials; Solitary Waves and Elastic Waves. Readership: Advanced undergraduate and graduate students as well as experts in mathematical modeling, engineering mechanics and mechanics, physics; specialists in wavelet and wave analysis as tools for mathematical modeling.
