An Introduction to Wavelet Analysis (Applied and Numerical Harmonic Analysis) - Hardcover

Walnut, David F.

Hardcover

ISBN 10: 0817639624 ISBN 13: 9780817639624

Publisher: Birkhäuser, 2001

Synopsis

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.

About this title

Review

"[This text] is carefully prepared, well-organized, and covers a large part of the central theory . . . [there are] chapters on biorthogonal wavelets and wavelet packets, topics which are rare in wavelet books. Both are important, and this feature is an extra argument in favour of [this] book . . . the material is accessible [even] to less advanced readers . . . the book is a nice addition to the series."   ―Zentralblatt Math

"This book can be recommended to everyone, especially to students looking for a detailed introduction to the subject."   ―Mathematical Reviews

"This textbook is an introduction to the mathematical theory of wavelet analysis at the level of advanced calculus. Some applications are described, but the main purpose of the book is to develop―using only tools from a first course in advanced calculus―a solid foundation in wavelet theory. It succeeds admirably. . . . Part I of the book contains 112 pages of preliminary material, consisting of four chapters on ‘Functions and Convergence,’ ‘Fourier Series,’ ‘Fourier Transforms,’ and ‘Signals and Systems.’ . . . This preliminary material is so well written that it could serve as an excellent supplement to a first course in advanced calculus. . . . The heart of the book is Part III: ‘Orthonormal Wavelet bases.’ This material has become the canonical portion of wavelet theory. Walnut does a first-rate job explaining the ideas here. . . . Ample references are supplied to aid the reader. . . . There are exercises at the end of each section, 170 in all, and they seem to be consistent with the level of the text. . . . To cover the whole book would require a year. An excellent one-semester course could be based on a selection of chapters from Parts II, III, and V."   ―SIAM Review

"D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!"   ―Bulletin of the AMS

Synopsis

A new text/reference offering a comprehensive and detailed presentation of wavelet theory, principles and methods. It presents basic theory of wavelet bases and transforms without assuming knowledge of advanced mathematics. The material is presented with many examples, exercises and thorough references. An essential text/reference for applied mathematicians, engineers and scientists. The goal of this book is to present the basics of wavelet theory in a complete, rigorous, and cogent fashion, but at a level that is truly appropriate for upper level undergraduates, first year graduate students, or anyone who has had a course in advanced calculus. The book presents the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book motivates the central ideas of wavelet theory by doing a detailed exposition of Haar series, and then shows how a more abstract approach allows us to generalize and improve upon Haar series. Once these ideas have been established and explored, variations and extensions of the Haar construction are presented.

Applications of the theory are to be stressed throughout the book as a means of motivating the usefulness of the theory, but a more complete treatment of applications will be saved for the last three chapters of the book. The book will also include exercises at the end of each chapter.

Edition details

• Publisher: Birkhäuser
• Publication date: 2001
• ISBN 10: 0817639624
• ISBN 13: 9780817639624
• Binding: Hardcover
• Language: English
• Number of pages: 472