Wavelets And Other Orthogonal Systems With Applications

Author : Gilbert G. Walter
Publisher : CRC Press
ISBN 13 : 1482285800
Total Pages : 391 pages
Book Rating : 4.02/5 ( download)

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Download or read book Wavelets and Other Orthogonal Systems written by Gilbert G. Walter and published by CRC Press. This book was released on 2018-10-03 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bestseller in its first edition, Wavelets and Other Orthogonal Systems: Second Edition has been fully updated to reflect the recent growth and development of this field, especially in the area of multiwavelets. The authors have incorporated more examples and numerous illustrations to help clarify concepts. They have also added a considerable amount of new material, including sections addressing impulse trains, an alternate approach to periodic wavelets, and positive wavelet s. Other new discussions include irregular sampling in wavelet subspaces, hybrid wavelet sampling, interpolating multiwavelets, and several new statistics topics. With cutting-edge applications in data compression, image analysis, numerical analysis, and acoustics wavelets remain at the forefront of current research. Wavelets and Other Orthogonal Systems maintains its mathematical perspective in presenting wavelets in the same setting as other orthogonal systems, thus allowing their advantages and disadvantages to be seen more directly. Now even more student friendly, the second edition forms an outstanding text not only for graduate students in mathematics, but also for those interested in scientific and engineering applications.

Author : Gilbert G. Walter
Publisher : CRC Press
ISBN 13 : 9780849378782
Total Pages : 264 pages
Book Rating : 4.88/5 ( download)

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Download or read book Wavelets and Other Orthogonal Systems with Applications written by Gilbert G. Walter and published by CRC Press. This book was released on 1994-07-13 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book makes accessible to both mathematicians and engineers important elements of the theory, construction, and application of orthogonal wavelets. It is integrated with more traditional orthogonal series, such as Fourier series and orthogonal polynomials. It treats the interaction of both with generalized functions (delta functions), which have played an important part in engineering theory but whose rules are often vaguely presented. Unlike most other books that are excessively technical, this text/reference presents the basic concepts and examples in a readable form. Much of the material on wavelets has not appeared previously in book form. Applications to statistics, sampling theorems, and stochastic processes are given. In particular, the close affinity between wavelets and sampling theorems is explained and developed.

Author : Peter Roberts
Publisher : New Age International
ISBN 13 : 9788122415155
Total Pages : 180 pages
Book Rating : 4.56/5 ( download)

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Download or read book Wavelet Analysis And Applications written by Peter Roberts and published by New Age International. This book was released on 2007 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets And Related Functions Constitute A Most Recent Set Of Mathematical Tools, Impacting Many Branches Of Mathematical And Applied Sciences, Ranging From Approximation Theory And Harmonic Analysis To Signal Analysis And Image Compression.This Volume Includes Lectures Delivered At The Platinum Jubilee Workshop And Tenth Ramanujan Symposium, Pjwtrs-2003, On Wavelet Analysis, Conducted In March 2003. The Contents Cover A Variety Of Interesting Topics Like Wavelets As Approximation Tools, Connections With Filter Banks, The Bessel-Wavelet Transform, Relations With Partial Differential Equations Of Fluid Flow, Weyl Heisenberg Frames, Reconstruction Of Functions From Irregular Sampling And Various Applications, Particularly In Electrical Engineering. This Book Will Be Useful To Mathematicians, Computer And Electrical Engineers, Systems Analysts And Applied Scientists. The Level Can Be Graduate Engineer Or Post Graduate Student Of Mathematics.

Author : Lokenath Debnath
Publisher : Springer
ISBN 13 : 0817684182
Total Pages : 562 pages
Book Rating : 4.81/5 ( download)

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Download or read book Wavelet Transforms and Their Applications written by Lokenath Debnath and published by Springer. This book was released on 2014-11-25 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals.

Author : John J. Benedetto
Publisher : CRC Press
ISBN 13 : 1000443469
Total Pages : 592 pages
Book Rating : 4.62/5 ( download)

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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.

Author : Lakshman Prasad
Publisher : CRC Press
ISBN 13 : 1000721981
Total Pages : 300 pages
Book Rating : 4.80/5 ( download)

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Download or read book Wavelet Analysis with Applications to Image Processing written by Lakshman Prasad and published by CRC Press. This book was released on 2020-01-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet analysis is among the newest additions to the arsenals of mathematicians, scientists, and engineers, and offers common solutions to diverse problems. However, students and professionals in some areas of engineering and science, intimidated by the mathematical background necessary to explore this subject, have been unable to use this powerful tool. The first book on the topic for readers with minimal mathematical backgrounds, Wavelet Analysis with Applications to Image Processing provides a thorough introduction to wavelets with applications in image processing. Unlike most other works on this subject, which are often collections of papers or research advances, this book offers students and researchers without an extensive math background a step-by-step introduction to the power of wavelet transforms and applications to image processing. The first four chapters introduce the basic topics of analysis that are vital to understanding the mathematics of wavelet transforms. Subsequent chapters build on the information presented earlier to cover the major themes of wavelet analysis and its applications to image processing. This is an ideal introduction to the subject for students, and a valuable reference guide for professionals working in image processing.

Author : Amir-Homayoon Najmi
Publisher : JHU Press
ISBN 13 : 1421405598
Total Pages : 303 pages
Book Rating : 4.99/5 ( download)

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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.

Author : James S. Walker
Publisher : CRC Press
ISBN 13 : 9780849382765
Total Pages : 168 pages
Book Rating : 4.69/5 ( download)

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Download or read book A Primer on Wavelets and Their Scientific Applications written by James S. Walker and published by CRC Press. This book was released on 1999-03-26 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques. Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data. Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLABä. Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned. Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background.

Author : David K. Ruch
Publisher : John Wiley & Sons
ISBN 13 : 1118165667
Total Pages : 502 pages
Book Rating : 4.69/5 ( download)

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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.

Author : Charles K. Chui
Publisher : Elsevier
ISBN 13 : 1483282864
Total Pages : 281 pages
Book Rating : 4.62/5 ( download)

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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 281 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.