Real Analysis With An Introduction To Wavelets And Applications
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Real Analysis With An Introduction To Wavelets And Applications
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Author : Don Hong
language : en
Publisher: Elsevier
Release Date : 2004-12-31
Real Analysis With An Introduction To Wavelets And Applications written by Don Hong and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-31 with Mathematics categories.
Real Analysis with an Introduction to Wavelets and Applications is an in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral, harmonic analysis and wavelet theory with many associated applications. The text is relatively elementary at the start, but the level of difficulty steadily increases The book contains many clear, detailed examples, case studies and exercises Many real world applications relating to measure theory and pure analysis Introduction to wavelet analysis
Wavelets
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Author : Peter Nickolas
language : en
Publisher: Cambridge University Press
Release Date : 2017-01-11
Wavelets written by Peter Nickolas and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-11 with Mathematics categories.
Makes the intrinsically advanced theory of wavelets accessible to senior undergraduate students with a mathematical background.
An Introduction To Wavelets
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Author : Charles K. Chui
language : en
Publisher: Elsevier
Release Date : 2016-06-03
An Introduction To Wavelets written by Charles K. Chui and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Science categories.
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.
Introduction To Fourier Analysis And Wavelets
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Author : Mark A. Pinsky
language : en
Publisher: American Mathematical Society
Release Date : 2023-12-21
Introduction To Fourier Analysis And Wavelets written by Mark A. Pinsky and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-21 with Mathematics categories.
This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches. The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs–Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere. Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces $L^p(mathbb{R}^n)$. Chapter 4 gives a gentle introduction to these results, using the Riesz–Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry–Esseen theorems are developed using the suitable Fourier-analytic tools. The final chapter furnishes a gentle introduction to wavelet theory, depending only on the $L_2$ theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis. The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.
Real Analysis
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Author : Jewgeni H. Dshalalow
language : en
Publisher: CRC Press
Release Date : 2000-09-28
Real Analysis written by Jewgeni H. Dshalalow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-28 with Mathematics categories.
Designed for use in a two-semester course on abstract analysis, REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration illuminates the principle topics that constitute real analysis. Self-contained, with coverage of topology, measure theory, and integration, it offers a thorough elaboration of major theorems, notions, and co
Multiresolution Signal And Geometry Processing Filter Banks Wavelets And Subdivision Version 2013 09 26
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Author : Michael D. Adams
language : en
Publisher: Michael Adams
Release Date : 2013-09-26
Multiresolution Signal And Geometry Processing Filter Banks Wavelets And Subdivision Version 2013 09 26 written by Michael D. Adams and has been published by Michael Adams this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Electric filters categories.
This book is intended for use in the teaching of graduate and senior undergraduate courses on multiresolution signal and geometry processing in the engineering and related disciplines. It has been used for several years for teaching purposes in the Department of Electrical and Computer Engineering at the University of Victoria and has been well received by students. This book provides a comprehensive introduction to multiresolution signal and geometry processing, with a focus on both theory and applications. The book has two main components, corresponding to multiresolution processing in the contexts of: 1) signal processing and 2) geometry processing. The signal-processing component of the book studies one-dimensional and multi-dimensional multirate systems, considering multirate structures such as sampling-rate converters, filter banks, and transmultiplexers. A particularly strong emphasis is placed on filter banks. Univariate and multivariate wavelet systems are examined, with the biorthogonal and orthonormal cases both being considered. The relationship between filter banks and wavelet systems is established. Several applications of filter banks and wavelets in signal processing are covered, including signal coding, image compression, and noise reduction. For readers interested in image compression, a detailed overview of the JPEG-2000 standard is also provided. Some other applications of multirate systems are considered, such as transmultiplexers for communication systems (e.g., multicarrier modulation). The geometry-processing component of the book studies subdivision surfaces and subdivision wavelets. Some mathematical background relating to geometry processing is provided, including topics such as homogeneous coordinate transformations, manifolds, surface representations, and polygon meshes. Several subdivision schemes are examined in detail, including the Loop, Kobbelt sqrt(3), and Catmull-Clark methods. The application of subdivision surfaces in computer graphics is considered. A detailed introduction to functional analysis is provided, for those who would like a deeper understanding of the mathematics underlying wavelets and filter banks. For those who are interested in software applications of the material covered in the book, appendices are included that introduce the CGAL and OpenGL libraries. Also, an appendix on the SPL library (which was developed for use with this book) is included. Throughout the book, many worked-through examples are provided. Problem sets are also provided for each major topic covered.
Framelets And Wavelets
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Author : Bin Han
language : en
Publisher: Springer
Release Date : 2018-01-04
Framelets And Wavelets written by Bin Han and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-04 with Mathematics categories.
Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide. As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises. Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets. Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.
A First Course In Wavelets With Fourier Analysis
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Author : Albert Boggess
language : en
Publisher: John Wiley & Sons
Release Date : 2015-08-21
A First Course In Wavelets With Fourier Analysis written by Albert Boggess and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-21 with Mathematics categories.
A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.
An Introduction To Wavelets
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Author : Charles K. Chui
language : en
Publisher: Elsevier
Release Date : 2014-06-28
An Introduction To Wavelets written by Charles K. Chui and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field. - This is an introductory treatise on wavelet analysis, with an emphasis on spline-wavelets and time-frequency analysis - This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis - Suitable as a textbook for a beginning course on wavelet analysis
Handbook Of Cancer Models With Applications
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Author : W. Y. Tan
language : en
Publisher: World Scientific
Release Date : 2008
Handbook Of Cancer Models With Applications written by W. Y. Tan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
Composed of contributions from an international team of leading researchers, this book pulls together the most recent research results in the field of cancer modeling to provide readers with the most advanced mathematical models of cancer and their applications.Topics included in the book cover oncogenetic trees, stochastic multistage models of carcinogenesis, effects of ionizing radiation on cell cycle and genomic instability, induction of DNA damage by ionizing radiation and its repair, epigenetic cancer models, bystander effects of radiation, multiple pathway models of human colon cancer, and stochastic models of metastasis. The book also provides some important applications of cancer models to the assessment of cancer risk associated with various hazardous environmental agents, to cancer screening by MRI, and to drug resistance in cancer chemotherapy. An updated statistical design and analysis of xenograft experiments as well as a statistical analysis of cancer occult clinical data are also provided.The book will serve as a useful source of reference for researchers in biomathematics, biostatistics and bioinformatics; for clinical investigators and medical doctors employing quantitative methods to develop procedures for cancer diagnosis, prevention, control and treatment; and for graduate students.