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Wavelets And Other Orthogonal Systems
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Book Synopsis Wavelets and Other Orthogonal Systems by : Gilbert G. Walter
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.
Book Synopsis Wavelets and Other Orthogonal Systems with Applications by : Gilbert G. Walter
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.
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 Wavelet Transforms and Their Applications by : Lokenath Debnath
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.
Book Synopsis Wavelet Radio by : Homayoun Nikookar
Download or read book Wavelet Radio written by Homayoun Nikookar and published by Cambridge University Press. This book was released on 2013-03-21 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to provide a detailed discussion of the application of wavelets in wireless communications, this is an invaluable source of information for graduate students, researchers, and telecommunications engineers, managers and strategists. It overviews applications, explains how to design new wavelets and compares wavelet technology with existing OFDM technology. • Addresses the applications and challenges of wavelet technology for a range of wireless communication domains • Aids in the understanding of Wavelet Packet Modulation and compares it with OFDM • Includes tutorials on convex optimisation, spectral factorisation and the design of wavelets • Explains design methods for new wavelet technologies for wireless communications, addressing many challenges, such as peak-to-average power ratio reduction, interference mitigation, reduction of sensitivity to time, frequency and phase offsets, and efficient usage of wireless resources • Describes the application of wavelet radio in spectrum sensing of cognitive radio systems.
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 An Introduction to Wavelet Analysis by : David F. Walnut
Download or read book An Introduction to Wavelet Analysis written by David F. Walnut and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Wavelet Theory by : Igor Iakovlevič Novikov (mathématicien).)
Download or read book Wavelet Theory written by Igor Iakovlevič Novikov (mathématicien).) and published by American Mathematical Soc.. This book was released on 2011 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet theory lies on the crossroad of pure and computational mathematics, with connections to audio and video signal processing, data compression, and information transmission. The present book is devoted to a systematic exposition of modern wavelet theory. It details the construction of orthogonal and biorthogonal systems of wavelets and studies their structural and approximation properties, starting with basic theory and ending with special topics and problems. The book also presents some applications of wavelets. Historical commentary is supplied for each chapter in the book, and most chapters contain exercises. The book is intended for professional mathematicians and graduate students working in functional analysis and approximation theory. It is also useful for engineers applying wavelet theory in their work. Prerequisites for reading the book consist of graduate courses in real and functional analysis.
Book Synopsis Wandering Vectors for Unitary Systems and Orthogonal Wavelets by : Xingde Dai
Download or read book Wandering Vectors for Unitary Systems and Orthogonal Wavelets written by Xingde Dai and published by American Mathematical Soc.. This book was released on 1998 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigates topological and structural properties of the set W(U) of all complete wandering vectors for a system U of unitary operators acting on a Hilbert space. The authors parameterize W(U) in terms of a fixed vector y and the set of all unitary operators which locally commute with U at y. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Wavelet Theory and Its Applications by : Randy K. Young
Download or read book Wavelet Theory and Its Applications written by Randy K. Young and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The continuous wavelet transform has deep mathematical roots in the work of Alberto P. Calderon. His seminal paper on complex method of interpolation and intermediate spaces provided the main tool for describing function spaces and their approximation properties. The Calderon identities allow one to give integral representations of many natural operators by using simple pieces of such operators, which are more suited for analysis. These pieces, which are essentially spectral projections, can be chosen in clever ways and have proved to be of tremendous utility in various problems of numerical analysis, multidimensional signal processing, video data compression, and reconstruction of high resolution images and high quality speech. A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject. These books, so far, are written by specialists for specialists, with a heavy mathematical flavor, which is characteristic of the Calderon-Zygmund theory and related research of Duffin-Schaeffer, Daubechies, Grossman, Meyer, Morlet, Chui, and others. Randy Young's monograph is geared more towards practitioners and even non-specialists, who want and, probably, should be cognizant of the exciting proven as well as potential benefits which have either already emerged or are likely to emerge from wavelet theory.
Book Synopsis Wavelet Analysis And Applications by : Peter Roberts
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.
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 Fundamental Papers in Wavelet Theory by : Christopher Heil
Download or read book Fundamental Papers in Wavelet Theory written by Christopher Heil and published by Princeton University Press. This book was released on 2006-07-23 with total page 897 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume traces the prehistory and initial development of wavelet theory, a discipline that has had a profound impact on mathematics, physics, and engineering. It contains the seminal papers that presented the ideas from which wavelet theory developed, as well as those papers that developed the theory.
Book Synopsis From Fourier Analysis to Wavelets by : Jonas Gomes
Download or read book From Fourier Analysis to Wavelets written by Jonas Gomes and published by Springer. This book was released on 2015-09-15 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
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 Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overview For over a decade now, wavelets have been and continue to be an evolving subject of intense interest. Their allure in signal processing is due to many factors, not the least of which is that they offer an intuitively satisfying view of signals as being composed of little pieces of wa'ues. Making this concept mathematically precise has resulted in a deep and sophisticated wavelet theory that has seemingly limitless applications. This book and its supplementary hands-on electronic: component are meant to appeal to both students and professionals. Mathematics and en gineering students at the undergraduate and graduate levels will benefit greatly from the introductory treatment of the subject. Professionals and advanced students will find the overcomplete approach to signal represen tation and processing of great value. In all cases the electronic component of the proposed work greatly enhances its appeal by providing interactive numerical illustrations. A main goal is to provide a bridge between the theory and practice of wavelet-based signal processing. Intended to give the reader a balanced look at the subject, this book emphasizes both theoretical and practical issues of wavelet processing. A great deal of exposition is given in the beginning chapters and is meant to give the reader a firm understanding of the basics of the discrete and continuous wavelet transforms and their relationship. Later chapters promote the idea that overcomplete systems of wavelets are a rich and largely unexplored area that have demonstrable benefits to offer in many applications.
Download or read book Wavelets written by Laura Montefusco and published by Elsevier. This book was released on 2014-06-28 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets: Theory, Algorithms, and Applications is the fifth volume in the highly respected series, WAVELET ANALYSIS AND ITS APPLICATIONS. This volume shows why wavelet analysis has become a tool of choice infields ranging from image compression, to signal detection and analysis in electrical engineering and geophysics, to analysis of turbulent or intermittent processes. The 28 papers comprising this volume are organized into seven subject areas: multiresolution analysis, wavelet transforms, tools for time-frequency analysis, wavelets and fractals, numerical methods and algorithms, and applications. More than 135 figures supplement the text. Features theory, techniques, and applicationsPresents alternative theoretical approaches including multiresolution analysis, splines, minimum entropy, and fractal aspectsContributors cover a broad range of approaches and applications
Book Synopsis Construction of Wavelets Through Walsh Functions by : Yu. A. Farkov
Download or read book Construction of Wavelets Through Walsh Functions written by Yu. A. Farkov and published by Springer. This book was released on 2019-04-29 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the fusion of wavelets and Walsh analysis, which involves non-trigonometric function series (or Walsh–Fourier series). The primary objective of the book is to systematically present the basic properties of non-trigonometric orthonormal systems such as the Haar system, Haar–Vilenkin system, Walsh system, wavelet system and frame system, as well as updated results on the book’s main theme. Based on lectures that the authors presented at several international conferences, the notions and concepts introduced in this interdisciplinary book can be applied to any situation where wavelets and their variants are used. Most of the applications of wavelet analysis and Walsh analysis can be tried for newly constructed wavelets. Given its breadth of coverage, the book offers a valuable resource for theoreticians and those applying mathematics in diverse areas. It is especially intended for graduate students of mathematics and engineering and researchers interested in applied analysis.
