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.

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.

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