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.

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.

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.

​In order to precisely model real-life systems or man-made devices, both nonlinear and dynamic properties need to be taken into account. The generic, black-box model based on Volterra and Wiener series is capable of representing fairly complicated nonlinear and dynamic interactions, however, the resulting identification algorithms are impractical, mainly due to their computational complexity. One of the alternatives offering fast identification algorithms is the block-oriented approach, in which systems of relatively simple structures are considered. The book provides nonparametric identification algorithms designed for such systems together with the description of their asymptotic and computational properties. ​ ​

Thema des Buches ist die Elementarwellen- (Wavelet-) -Theorie (Zeit-Frequenz-Analyse), ein Grenzgebiet zwischen Mathematik und Ingenieurwissenschaften. - viele Anwendungen in der Elektronik, darunter Antennentheorie und drahtlose Kommunikation - erstes Buch, das die Wavelet-Theorie auf elektromagnetische Phänomene und auf die Modellierung von Halbleiterbauelementen anwendet

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.

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

Wavelet Transforms: Kith and Kin serves as an introduction to contemporary aspects of time-frequency analysis encompassing the theories of Fourier transforms, wavelet transforms and their respective offshoots. This book is the first of its kind totally devoted to the treatment of continuous signals and it systematically encompasses the theory of Fourier transforms, wavelet transforms, geometrical wavelet transforms and their ramifications. The authors intend to motivate and stimulate interest among mathematicians, computer scientists, engineers and physical, chemical and biological scientists. The text is written from the ground up with target readers being senior undergraduate and first-year graduate students and it can serve as a reference for professionals in mathematics, engineering and applied sciences. Features Flexibility in the book’s organization enables instructors to select chapters appropriate to courses of different lengths, emphasis and levels of difficulty Self-contained, the text provides an impetus to the contemporary developments in the signal processing aspects of wavelet theory at the forefront of research A large number of worked-out examples are included Every major concept is presented with explanations, limitations and subsequent developments, with emphasis on applications in science and engineering A wide range of exercises are incoporated in varying levels from elementary to challenging so readers may develop both manipulative skills in theory wavelets and deeper insight Answers and hints for selected exercises appear at the end The origin of the theory of wavelet transforms dates back to the 1980s as an outcome of the intriguing efforts of mathematicians, physicists and engineers. Owing to the lucid mathematical framework and versatile applicability, the theory of wavelet transforms is now a nucleus of shared aspirations and ideas.

This comprehensive volume develops all of the standard features of Fourier analysis - Fourier series, Fourier transform, Fourier sine and cosine transforms, and wavelets. The books approach emphasizes the role of the "selector" functions, and is not embedded in the usual engineering context, which makes the material more accessible to a wider audience. While there are several publications on the various individual topics, none combine or even include all of the above.

This book presents the basic concepts of functional analysis, wavelet analysis and thresholding. It begins with an elementary chapter on preliminaries such as basic concepts of functional analysis, a brief tour of the wavelet transform, Haar scaling functions and function space, wavelets, symlets wavelets and coiflets wavelets. In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds. Chapter 4 discusses characterisations of function spaces like Lebesgue spaces, Hardy spaces and Sobolev spaces in terms of wavelet packets, while Chapter 5 is devoted to applications of wavelets and wavelet packets in speech denoising and biomedical signals. In closing, Chapter 6 highlights applications of wavelets and wavelet packets in image denoising.