Wavelet Transforms and Time-Frequency Signal Analysis

1. Front Matter

   Pages i-xx

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2. Wavelets and Wavelet Transforms

   1. Front Matter

      Pages 1-1

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   2. Wavelet Frames: Multiresolution Analysis and Extension Principles

      • John J. Benedetto, Oliver M. Treiber

      Pages 3-36

   3. Convergence Rates of Multiscale and Wavelet Expansions

      • Mark A. Kon, Louise Arakelian Raphael

      Pages 37-65

   4. Denoising via Nonorthogonal Wavelet Transforms

      • Kathrin Berkner, Raymond O. Wells Jr.

      Pages 67-80

   5. Osiris Wavelets and the Dipole Gas

      • Guy Battle

      Pages 81-120

   6. Wavelets in Closed Forms

      • Ahmed I. Zayed, Gilbert G. Walter

      Pages 121-143

   7. Wavelet Galerkin Methods for Boundary Integral Equations and the Coupling with Finite Element Methods

      • Cristian Pérez, Reinhold Schneider

      Pages 145-179

   8. Computing and Analyzing Turbulent Flows Using Wavelets

      • Kai Schneider, Marie Farge

      Pages 181-216

   9. The Uncertainty Principle for the Short-Time Fourier Transform and Wavelet Transform

      • Leon Cohen

      Pages 217-232

3. Time-Frequency Signal Analysis

   1. Front Matter

      Pages 233-233

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   2. Quadratic Time-Frequency Analysis of Linear Time-Varying Systems

      • Franz Hlawatsch, Gerald Matz

      Pages 235-287

   3. Inequalities in Mellin-Fourier Signal Analysis

      • Patrick Flandrin

      Pages 289-319

   4. Introduction to Time-Frequency Signal Analysis

      • Boualem Boashash, Braham Barkat

      Pages 321-380

   5. Reduced Interference Time-Frequency Distributions: Scaled Decompositions and Interpretations

      • William J. Williams

      Pages 381-417

4. Back Matter

   Pages 419-425

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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.

• Fourier analysis
• Fourier transform
• Signal
• Wavelet
• calculus
• electrical engineering
• signal analysis
• signal processing
• statistics
• uncertainty
• wavelets

"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

• Department of Mathematics, University of Central Florida, Orlando, USA

  Lokenath Debnath

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