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Author: Y. T. Chan
Publisher: Springer Science & Business Media
ISBN: 1461522137
Category : Science
Languages : en
Pages : 139
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Book Description
Since the study of wavelets is a relatively new area, much of the research coming from mathematicians, most of the literature uses terminology, concepts and proofs that may, at times, be difficult and intimidating for the engineer. Wavelet Basics has therefore been written as an introductory book for scientists and engineers. The mathematical presentation has been kept simple, the concepts being presented in elaborate detail in a terminology that engineers will find familiar. Difficult ideas are illustrated with examples which will also aid in the development of an intuitive insight. Chapter 1 reviews the basics of signal transformation and discusses the concepts of duals and frames. Chapter 2 introduces the wavelet transform, contrasts it with the short-time Fourier transform and clarifies the names of the different types of wavelet transforms. Chapter 3 links multiresolution analysis, orthonormal wavelets and the design of digital filters. Chapter 4 gives a tour d'horizon of topics of current interest: wavelet packets and discrete time wavelet transforms, and concludes with applications in signal processing.
Author: Y. T. Chan
Publisher: Springer Science & Business Media
ISBN: 1461522137
Category : Science
Languages : en
Pages : 139
Get Book Here
Book Description
Since the study of wavelets is a relatively new area, much of the research coming from mathematicians, most of the literature uses terminology, concepts and proofs that may, at times, be difficult and intimidating for the engineer. Wavelet Basics has therefore been written as an introductory book for scientists and engineers. The mathematical presentation has been kept simple, the concepts being presented in elaborate detail in a terminology that engineers will find familiar. Difficult ideas are illustrated with examples which will also aid in the development of an intuitive insight. Chapter 1 reviews the basics of signal transformation and discusses the concepts of duals and frames. Chapter 2 introduces the wavelet transform, contrasts it with the short-time Fourier transform and clarifies the names of the different types of wavelet transforms. Chapter 3 links multiresolution analysis, orthonormal wavelets and the design of digital filters. Chapter 4 gives a tour d'horizon of topics of current interest: wavelet packets and discrete time wavelet transforms, and concludes with applications in signal processing.
Author: Charles K. Chui
Publisher: Elsevier
ISBN: 1483282864
Category : Science
Languages : en
Pages : 281
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Book Description
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.
Author: David F. Walnut
Publisher: Springer Science & Business Media
ISBN: 1461200016
Category : Computers
Languages : en
Pages : 453
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Book Description
This book provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and analysis of wavelet bases. It motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, then shows how a more abstract approach allows readers to generalize and improve upon the Haar series. It then presents a number of variations and extensions of Haar construction.
Author: C. S. Burrus
Publisher: Pearson
ISBN:
Category : Mathematics
Languages : en
Pages : 294
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Book Description
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.
Author: Mani Mehra
Publisher: Springer
ISBN: 9811325952
Category : Mathematics
Languages : en
Pages : 185
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Book Description
This book provides comprehensive information on the conceptual basis of wavelet theory and it applications. Maintaining an essential balance between mathematical rigour and the practical applications of wavelet theory, the book is closely linked to the wavelet MATLAB toolbox, which is accompanied, wherever applicable, by relevant MATLAB codes. The book is divided into four parts, the first of which is devoted to the mathematical foundations. The second part offers a basic introduction to wavelets. The third part discusses wavelet-based numerical methods for differential equations, while the last part highlights applications of wavelets in other fields. The book is ideally suited as a text for undergraduate and graduate students of mathematics and engineering.
Author: M.W. Frazier
Publisher: Springer
ISBN: 3642855709
Category : Mathematics
Languages : en
Pages : 517
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Book Description
Mathematics majors at Michigan State University take a "Capstone" course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basic wavelet theory is a natural topic for such a course. By name, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are sufficiently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity.
Author: Nirdosh Bhatnagar
Publisher: CRC Press
ISBN: 1000768619
Category : Computers
Languages : en
Pages : 484
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Book Description
The textbook, Introduction to Wavelet Transforms provides basics of wavelet transforms in a self-contained manner. Applications of wavelet transform theory permeate our daily lives. Therefore it is imperative to have a strong foundation for this subject. Features No prior knowledge of the subject is assumed. Sufficient mathematical background is provided to complete the discussion of different topics. Different topics have been properly segmented for easy learning. This makes the textbook pedagogical and unique. Notation is generally introduced in the definitions. Relatively easy consequences of the definitions are listed as observations, and important results are stated as theorems. Examples are provided for clarity and to enhance reader's understanding of the subject. Each chapter also has a problem section. A majority of the problems are provided with sufficient hints. The textbook can be used either in an upper-level undergraduate or first-year graduate class in electrical engineering, or computer science, or applied mathematics. It can also be used by professionals and researchers in the field who would like a quick review of the basics of the subject. About the Author Nirdosh Bhatnagar works in both academia and industry in Silicon Valley, California. He is also the author of a comprehensive two-volume work: Mathematical Principles of the Internet, published by the CRC Press in the year 2019. Nirdosh earned M.S. in Operations Research, and M.S. and Ph.D. in electrical engineering, all from Stanford University, Stanford, California.
Author: Jaideva C. Goswami
Publisher: John Wiley & Sons
ISBN: 0470934646
Category : Computers
Languages : en
Pages : 310
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Book Description
Most existing books on wavelets are either too mathematical or they focus on too narrow a specialty. This book provides a thorough treatment of the subject from an engineering point of view. It is a one-stop source of theory, algorithms, applications, and computer codes related to wavelets. This second edition has been updated by the addition of: a section on "Other Wavelets" that describes curvelets, ridgelets, lifting wavelets, etc a section on lifting algorithms Sections on Edge Detection and Geophysical Applications Section on Multiresolution Time Domain Method (MRTD) and on Inverse problems
Author: P. Wojtaszczyk
Publisher: Cambridge University Press
ISBN: 9780521578943
Category : Mathematics
Languages : en
Pages : 280
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Book Description
The only introduction to wavelets that doesn't avoid the tough mathematical questions.
Author: Patrick J. Van Fleet
Publisher: John Wiley & Sons
ISBN: 1118979273
Category : Mathematics
Languages : en
Pages : 637
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Book Description
Updated and Expanded Textbook Offers Accessible and Applications-First Introduction to Wavelet Theory for Students and Professionals The new edition of Discrete Wavelet Transformations continues to guide readers through the abstract concepts of wavelet theory by using Dr. Van Fleet’s highly practical, application-based approach, which reflects how mathematicians construct solutions to challenges outside the classroom. By introducing the Haar, orthogonal, and biorthogonal filters without the use of Fourier series, Van Fleet allows his audience to connect concepts directly to real-world applications at an earlier point than other publications in the field. Leveraging extensive graphical displays, this self-contained volume integrates concepts from calculus and linear algebra into the constructions of wavelet transformations and their applications, including data compression, edge detection in images and denoising of signals. Conceptual understanding is reinforced with over 500 detailed exercises and 24 computer labs. The second edition discusses new applications including image segmentation, pansharpening, and the FBI fingerprint compression specification. Other notable features include: Two new chapters covering wavelet packets and the lifting method A reorganization of the presentation so that basic filters can be constructed without the use of Fourier techniques A new comprehensive chapter that explains filter derivation using Fourier techniques Over 120 examples of which 91 are “live examples,” which allow the reader to quickly reproduce these examples in Mathematica or MATLAB and deepen conceptual mastery An overview of digital image basics, equipping readers with the tools they need to understand the image processing applications presented A complete rewrite of the DiscreteWavelets package called WaveletWare for use with Mathematica and MATLAB A website, www.stthomas.edu/wavelets, featuring material containing the WaveletWare package, live examples, and computer labs in addition to companion material for teaching a course using the book Comprehensive and grounded, this book and its online components provide an excellent foundation for developing undergraduate courses as well as a valuable resource for mathematicians, signal process engineers, and other professionals seeking to understand the practical applications of discrete wavelet transformations in solving real-world challenges.
