Wavelets: Time-Frequency Methods and Phase Space

ISBN-13: 9783642971792 / Angielski / Miękka / 2012 / 315 str.

Jean-Michel Combes; Alexander Grossmann; Philippe Tchamitchian

Opis

The last two subjects mentioned in the title "Wavelets" are so well established that they do not need any explanations. The first is related to them, but a short introduction is appropriate since the concept of wavelets emerged fairly recently. Roughly speaking, a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position pa rameter. Many of the ideas and techniques related to such expansions have existed for a long time and are widely used in mathematical analysis, theoretical physics and engineering. However, the rate of progress increased significantly when it was realized that these ideas could give rise to straightforward calculational methods applicable to different fields. The interdisciplinary structure (R.c.P. "Ondelettes") of the C.N .R.S. and help from the Societe Nationale Elf-Aquitaine greatly fostered these developments. This conference was held at the Centre National de Rencontres Mathematiques (C.I.R.M) in Marseille from December 14 to 18, 1987 and brought together an interdisciplinary mix of participants. We hope that these proceedings will convey to the reader some of the excitement and flavor of the meeting."

Spis treści

I Introduction to Wavelet Transforms.- Reading and Understanding Continuous Wavelet Transforms.- Orthonormal Wavelets.- Orthonormal Bases of Wavelets with Finite Support — Connection with Discrete Filters.- II Some Topics in Signal Analysis.- Some Aspects of Non-Stationary Signal Processing with Emphasis on Time-Frequency and Time-Scale Methods.- Detection of Abrupt Changes in Signal Processmg.- The Computer, Music, and Sound Models.- III Wavelets and Signal Processing.- Wavelets and Seismic Interpretation.- Wavelet Transformations in Signal Detection.- Use of Wavelet Transforms in the Smdy of Propagation of Transient Acoustic Signals Across a Plane Interface Between Two Homogeneous Media.- Time-Frequency Analysis of Signals Related to Scattering Problems in Acoustics Part I: Wigner-Ville Analysis of Echoes Scattered by a Spherical Shell.- Coherence and Projectors in Acoustics.- Wavelets and Granular Analysis of Speech.- Time-Frequency Representations of Broad-Band Signals.- Operator Groups and Ambiguity Functions in Signal Processing.- IV Mathematics and Mathematical Physics.- Wavelet Transform Analysis of Invariant Measures of Some Dynamical Systems.- Holomorphic Integral Representations for the Solutions of the Hehnholtz Equation.- Wavelets and Path Integral.- Mean Value Theorems and Concentration Operators in Bargmann and Bergman Space.- Besov Sobolev Algebras of Symbols.- Poincaré Coherent States and Relativistic Phase Space Analysis.- A Relativistic Wigner Function Affiliated with the Weyl-Poincaré Group.- Wavelet Transforms Associated to the n-Dimensional Euclidean Group with Dilations: Signal in More Than One Dimension.- Construction of Wavelets on Open Sets.- Wavelets on Chord-Arc Curves.- Multiresolution Analysis in Non-Homogeneous Media.- About Wavelets and Elliptic Operators.- Towards a Method for Solving Partial Differential Equations Using Wavelet Bases.- V Implementations.- A Real-Time Algorithm for Signal Analysis with the Help of the Wavelet Transform.- An Implementation of the “algorithme k trous” to Compute the Wavelet Transform.- An Algorithm for Fast Imaging of Wavelet Transforms.- Index of Contributors.