Book Description

Wavelets is a new area that stands at the intersection of the frontiers of mathematics, scientific computing, and signal and image processing, and is one of the major research directions in science in the last decade which is still undergoing rapid growth. This book brings together eleven of the polished versions of the seminars and lectures held over a year-long programme on "Wavelets and their Applications" in Hong Kong, and which cumulated to a workshop in May 1997 which was attended by scientists and graduate students from China, Singapore, North and South America, and Europe. The volume covers the topics of: Theory of frames and applications; Wavelet coefficients; Refinable functions and approximation; Multiwavelets; and Tiling. . Advances in Wavelets will prove a useful reference source to graduate students and researchers alike on the many applications of wavelets. ... Read more

Reviews (1)

Great collection.
While there is a variety of collections of wavelet papers, presenting the state of the art, in some of the many facets of the subject, this lovely book stands out.-- One of the best! The collection of authors, and the quality of the papers, are great. The material is timeless, and the book will be of use for many years to come. ... Read more

Book Description

Nowadays, some knowledge of wavelets is almost mandatory for mathematicians, physicists and electrical engineers. The emphasis in this volume, based on an intensive course on Wavelets given at CWI, Amsterdam, is on the affine case. The first part presents a concise introduction of the underlying theory to the uninitiated reader. The second part gives applications in various areas. Some of the contributions here are a fresh exposition of earlier work by others, while other papers contain new results by the authors. The areas are so diverse as seismic processing, quadrature formulae, and wavelet bases adapted to inhomogeneous cases. ... Read more

Book Description

With applications in pattern recognition, data compression and numerical analysis, the wavelet transform is a key area of modern mathematics that brings new approaches to the analysis and synthesis of signals. This book presents the central issues and emphasizes comparison, assessment and how to combine method and application. It reviews different approaches to guide researchers to appropriate classes of techniques. ... Read more

Book Description

Based on the Sixth International Workshop in Analysis and Its Applications held recently at the University of Maine, this useful volume provides complete expository and research papers on the geometric and analytic aspects of Fourier analysis.Containing the authoritative contributions of more than 25 world experts, Fourier Analysis discusses new approaches to classical problems in the theory of trigonometric series singular integrals/pseudodifferential operators Fourier analysis on various groups numerical aspects of Fourier analysis and their applications wavelets and more! ... Read more

Book Description

The purpose of this book is to describe a certain number of results involving the study of non-linear analytic dependence of some functionals arising naturally in P.D.E. or operator theory. ... Read more

Book Description

This short reference provides four in-depth reference tutorials on the FFT: Fourier transforms, including Fourier series and discrete Fourier transforms, the Cooley-Tukey algorithm, the bit-reverse index reordering problem and two of its solutions, and spectral windows. Each area has problems of various scopes and difficulties designed to provoke thought and curiosity, and to illuminate the topic in ways not always presented in the text. The scope of the material is specifically intended to apply to applications for the foreseeable future as well as provide a reference for applications that have not yet emerged, such as 3-D processing of multiple parallel data streams for true time-delay broadband beamforming and ambiguity resolution using sparse arrays. This scope is supported through a unified treatment of one, two, and three-dimensional FFTs with seamless extension to higher dimensionality. The section on spectral window weighting is alone worth the book, as it provides a unified in-depth tutorial, including many plots, of all commonly used one-dimensional and two-dimensional spectral weightings, with extensions to higher dimensionality. Several new high-performance spectral weights are introduced, including a monopulse weighting for planar arrays with good antenna efficiency and excellent sidelobe control that is based on Chebychev polynomials of the second kind, and a five-cosine extension to the Blackman-Harris window with 118 dB performance. This unified treatment will leave you in complete command of the theory, algorithm, and signal processing trade space in areas where the FFT is used for the present and for many years into the future. ... Read more

Book Description

Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated, however there exists a rule which generates the sequence. The concept automatic sequences has special applications in algebra, number theory, finite automata and formal languages, combinatorics on words.

The text deals with different aspects of automatic sequences, in particular:

• a general introduction to automatic sequences
• the basic (combinatorial) properties of automatic sequences
• the algebraic approach to automatic sequences
• geometric objects related to automatic sequences. ... Read more

Book Description

This book constitutes the refereed proceedings of the Second International Conference on Wavelet Analysis and Its Applications, WAA 2001, held in Hong Kong, China in December 2001. The 24 revised full papers and 27 revised short papers presented were carefully reviewed and selected from a total of 67 full paper submissions. The book offers topical sections on image compression and coding, video coding and processing, theory, image processing, signal processing, and systems and applications. ... Read more

Book Description

Hardbound. This book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems. ... Read more

Book Description

Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz’s proof of the isoperimetric inequality using Fourier series.                                                             This unified, self-contained volume is dedicated to Fourier analysis, convex geometry, and related topics. Specific topics covered include:* the geometric properties of convex bodies * the study of Radon transforms * the geometry of numbers * the study of translational tilings using Fourier analysis * irregularities in distributions * Lattice point problems examined in the context of number theory, probability theory, and Fourier analysis * restriction problems for the Fourier transform  The book presents both a broad overview of Fourier analysis and convexity as well as an intricate look at applications in some specific settings; it will be useful to graduate students and researchers in harmonic analysis, convex geometry, functional analysis, number theory, computer science, and combinatorial analysis. A wide audience will benefit from the careful demonstration of how Fourier analysis is used to distill the essence of many mathematical problems in a natural and elegant way. Contributors: J. Beck, C. Berenstein, W.W.L. Chen, B. Green, H. Groemer, A. Koldobsky, M. Kolountzakis, A. Magyar, A.N. Podkorytov, B. Rubin, D. Ryabogin, T. Tao, G. Travaglini, A. Zvavitch ... Read more