Download or read book Wavelet Analysis on the Sphere written by Sabrine Arfaoui and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-20 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to develop the theory of wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials.
Download or read book Wavelet Analysis on the Sphere written by Sabrine Arfaoui and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-03-20 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to develop the theory of wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials.
Download or read book Wavelets in the Geosciences written by Roland Klees and published by Springer Science & Business Media. This book was released on 2000-03-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains state-of-the-art continuous wavelet analysis of one and more dimensional (geophysical) signals. Special attention is given to the reconaissance of specific properties of a signal. It also contains an extension of standard wavelet approximation to the application of so-called second generation wavelets for efficient representation of signals at various scales even on the sphere and more complex geometries. Furthermore, the book discusses the application of harmonic (spherical) wavelets in potential field analysis with emphasis on the gravity field of the Earth. Many examples are given for practical application of these tools; to support the text exercises and demonstrations are available on the Web.
Download or read book Wavelets in the Geosciences written by Roland Klees and published by Springer. This book was released on 2014-03-12 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains state-of-the-art continuous wavelet analysis of one and more dimensional (geophysical) signals. Special attention is given to the reconaissance of specific properties of a signal. It also contains an extension of standard wavelet approximation to the application of so-called second generation wavelets for efficient representation of signals at various scales even on the sphere and more complex geometries. Furthermore, the book discusses the application of harmonic (spherical) wavelets in potential field analysis with emphasis on the gravity field of the Earth. Many examples are given for practical application of these tools; to support the text exercises and demonstrations are available on the Web.
Download or read book Wavelt Analysis and Spline Modeling of Geophysical Data on the Sphere written by Michael Hayn and published by . This book was released on 2010 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Wavelets in Geodesy and Geodynamics written by Wolfgang Keller and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many years, digital signal processing has been governed by the theory of Fourier transform and its numerical implementation. The main disadvantage of Fourier theory is the underlying assumption that the signals have time-wise or space-wise invariant statistical properties. In many applications the deviation from a stationary behavior is precisely the information to be extracted from the signals. Wavelets were developed to serve the purpose of analysing such instationary signals. The book gives an introduction to wavelet theory both in the continuous and the discrete case. After developing the theoretical fundament, typical examples of wavelet analysis in the Geosciences are presented. The book has developed from a graduate course held at The University of Calgary and is directed to graduate students who are interested in digital signal processing. The reader is assumed to have a mathematical background on the graduate level.
Download or read book Thoughts on Harmonic Analysis on the Sphere Spherical Wavelet Frames and Kernels written by Yizhi Sun and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Two Dimensional Wavelets and their Relatives written by Jean-Pierre Antoine and published by Cambridge University Press. This book was released on 2008-06-12 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms, in particular for analysis of real-time signals. This book provides thorough and comprehensive treatment of 2-D wavelets, with extensive use of practical applications and illustrative examples throughout. For engineers, physicists and mathematicians.
Download or read book Wavelet Analysis written by Sabrine Arfaoui and published by CRC Press. This book was released on 2021-04-20 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet Analysis: Basic Concepts and Applications provides a basic and self-contained introduction to the ideas underpinning wavelet theory and its diverse applications. This book is suitable for master’s or PhD students, senior researchers, or scientists working in industrial settings, where wavelets are used to model real-world phenomena and data needs (such as finance, medicine, engineering, transport, images, signals, etc.). Features: Offers a self-contained discussion of wavelet theory Suitable for a wide audience of post-graduate students, researchers, practitioners, and theorists Provides researchers with detailed proofs Provides guides for readers to help them understand and practice wavelet analysis in different areas
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.
Download or read book Wavelet Analysis and Applications written by Tao Qian and published by Springer Science & Business Media. This book was released on 2007-02-24 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.
Download or read book Generalized Wavelets and Hypergroups written by Khalifa Trimeche and published by CRC Press. This book was released on 1997-10-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets have recently been enjoying a period of popularity and rapid growth, and the influence of wavelet methods now extends well beyond mathematics into a number of practical fields, including statistics. The theory of hypergroups can be traced back to the turn of the century, and following its formalization in the early 1970s, the area has now reached maturity. Hypergroups provide a very general and flexible context in which many of the classical techniques of harmonic analysis can be fruitfully employed. It is, therefore, natural to seek to exploit the newer techniques of wavelet analysis in this area. This text addresses itself to this challenge in some depth, providing a thorough and authoritative account of wavelet methods applied to hypergroups.
Download or read book Lectures on Constructive Approximation written by Volker Michel and published by Springer Science & Business Media. This book was released on 2012-12-12 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.
Download or read book Wavelet Transforms and Their Applications written by Lokenath Debnath and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overview Historically, the concept of "ondelettes" or "wavelets" originated from the study of time-frequency signal analysis, wave propagation, and sampling theory. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean MorIet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals. However, this new concept can be viewed as the synthesis of various ideas originating from different disciplines including mathematics (Calder6n-Zygmund operators and Littlewood-Paley theory), physics (coherent states in quantum mechanics and the renormalization group), and engineering (quadratic mirror filters, sideband coding in signal processing, and pyramidal algorithms in image processing). Wavelet analysis is an exciting new method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines, and improvement in CAT scans and other medical image technology. Wavelets allow complex information such as music, speech, images, and patterns to be decomposed into elementary forms, called the fundamental building blocks, at different positions and scales and subsequently reconstructed with high precision.
Download or read book Introduction to Fourier Analysis and Wavelets written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2008 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text 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. It contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.
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.
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.