### Synopses & Reviews

The last two decades have produced tremendous developments in the mathematical theory of wavelets and their great variety of applications in science and engineering. Wavelets allow complex information, such as music, speech, images, and patterns, to be decomposed into an elementary form called building blocks at different positions and scales. The information is reconstructed with high precision. In an effort to acquaint researchers in applied mathematics, physics, statistics, computer science, and engineering and to stimulate further research, a regional research conference was organized at the University of Central Florida in May 1998. Many distinguished applied mathematicians and engineering scientists participated in the conference and presented a digest of recent developments, open questions, and unsolved problems in this rapidly growing and important field. The carefully selected chapters in this new text will appeal to the reader interested in a broad perspective of wavelet analysis and time-frequency signal analysis. Wavelet Transforms and Time-Frequency Signal Analysis brings together recent developments in theory and applications of wavelet transforms that are likely to determine fruitful directions for future advanced study and research. The book is designed as a new source for modern topics dealing with wavelets, wavelet transforms, time-frequency signal analysis, and other applications for future development of this new, important, and useful subject for mathematics, science and engineering. Topics and Features: * Offers broad coverage of recent material on wavelet analysis and time-frequency signal analysis that is not covered in other recent reference books * Provides the reader with a thorough mathematical background and a wide variety of applications that are sufficient for interdisciplinary collaborative research in applied mathematics * Presents information that puts the reader at the forefront of current research Wavelet Transforms and Time-Frequency Signal Analysis will serve as a research reference or as a text for an advanced course in wavelet analysis and time-frequency signal analysis. Professionals working on modern applied mathematics, computer science, computer engineering, electrical engineering, physics, and biomedical engineering will also find this book useful.

#### Review

"This book is a great collection of recent material of recent investigation on wavelet and time-frequency analysis that is not covered in the literature.... The book is an important source for all readers interested in a broad perspective. In particular, a wide variety of applications are presented that are important for interdisciplinary collaborative research." --ZAA

#### Synopsis

The last fifteen years have produced major advances in the mathematical theory of wavelet transforms and their applications to science and engineering. In an effort to inform researchers in mathematics, physics, statistics, computer science, and engineering and to stimulate furtherresearch, an NSF-CBMS Research Conference on Wavelet Analysis was organized at the University of Central Florida in May 1998. Many distinguished mathematicians and scientists from allover the world participated in the conference and provided a digest of recent developments, open questions, and unsolved problems in this rapidly growing and important field. As a follow-up project, this monograph was developed from manuscripts sub- mitted by renowned mathematicians and scientists who have made important contributions to the subject of wavelets, wavelet transforms, and time-frequency signal analysis. This publication brings together current developments in the theory and applications of wavelet transforms and in the field of time-frequency signal analysis that are likely to determine fruitful directions for future advanced study and research.

#### Synopsis

This volume is designed as a new source for modern topics dealing with wavelets, wavelet transforms time-frequency signal analysis and other applications for future development of this new, important and useful subject for mathematics, science and engineering. Its main features include: A broad coverage of recent material on wavelet analysis, and time-frequency signal analysis and other applications that are not usually covered in other recent reference books. The material presented in this volume brings together a rich variety of ideas that blend most aspects of the subject mentioned above. This volume brings together a detailed account of major recent developments in wavelets, wavelet transforms and time-frequency signal analysis. This volume provides the reader with a thorough mathematical background and a wide variety of applications that are sufficient to do interdisciplinary collaborative research in applied mathematics. The book provides information that puts the reader at the forefront of the current resarch. An up-to-date bibliography is included at the end of each chapter to stimulate new interest in future study and research.

### Table of Contents

Preface

Contributors

Color Insert

I. Wavelets and Wavelet Transforms

Wavelet Frames: Multiresolution Analysis and Extension Principles \ J.J. Benedetto and O.M. Treiber

Convergence Rates of Multiscale and Wavelet Expansions \ M.A. Kon and L.A. Raphael

Denoising via Nonorthogonal Wavelet Transforms \ K. Berkner and R.O. Wells, Jr.

Osiris Wavelets and the Dipole Gas \ G. Battle

Wavelets in Closed Forms \ A. Zayed and G.G. Walter

Wavelet Galerkin Methods for Boundary Integral Equations and the Coupling with Finite Element Methods \ C. Pérez and R. Schneider

Computing and Analyzing Turbulent Flows Using Wavelets \ K. Schneider and M. Farge

The Uncertainty Principle for the Short-Time Fourier Transform and Wavelet Transform \ L. Cohen

II. Time-Frequency Signal Analysis

Quadratic Time-Frequency Analysis of Linear, Time-Varying Systems \ F. Hlawatsch and G. Matz

Inequalities in Mellin--Fourier Signal Analysis \ P. Flandrin

Introduction to Time-Frequency Signal Analysis \ B. Boashash and B. Barkat

Reduced Interference Time-Frequency Distributions: Scaled Decompositions and Interpretations / W.J. Williams

Index