Wavelet Transforms and Time-Frequency Signal Analysis, Softcover reprint of the original 1st ed. 2001 Applied and Numerical Harmonic Analysis Series

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.

I Wavelets and Wavelet Transforms.- 1 Wavelet Frames: Multiresolution Analysis and Extension Principles.- 2 Convergence Rates of Multiscale and Wavelet Expansions.- 3 Denoising via Nonorthogonal Wavelet Transforms.- 4 Osiris Wavelets and the Dipole Gas.- 5 Wavelets in Closed Forms.- 6 Wavelet Galerkin Methods for Boundary Integral Equations and the Coupling with Finite Element Methods.- 7 Computing and Analyzing Turbulent Flows Using Wavelets.- 8 The Uncertainty Principle for the Short-Time Fourier Transform and Wavelet Transform.- II Time-Frequency Signal Analysis.- 9 Quadratic Time-Frequency Analysis of Linear Time-Varying Systems.- 10 Inequalities in Mellin—Fourier Signal Analysis.- 11 Introduction to Time-Frequency Signal Analysis.- 12 Reduced Interference Time-Frequency Distributions: Scaled Decompositions and Interpretations.