Wavelets : time-frequency methods and phase space : proceedings of the international conference, Marseille, France, December 14-18, 1987

J.M. Combes, A. Grossmann, Ph. Tchamitchian, (eds.)

Time-frequency methods and phase space are well known to most physicists, engineers and mathematicians as is the traditional Fourier analysis. Recently the latter found for quite a few applications a competitor in the concept of wavelets. Crudely speaking a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position parameter. This meeting brought together people exploring and applying these concepts in an interdisciplinary framework. The topics discussed range from purely mathematical aspects over signal analysis, seismic and acoustic applications via animal sonar systems to wavelets in computer vision.

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  • 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 Processing.- 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 Study 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 Helmholtz Equation.- Wavelets and Path Integrals.- Mean Value Theorems and Concentration Operators in Bargmann and Bergman Space.- Besov-Sobolev Algebras of Symbols.- Poincare Coherent States and Relativistic Phase Space Analysis.- A Relativistic Wigner Function Affiliated with the Weyl-Poincare 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 a trous" to Compute the Wavelet Transform.- An Algorithm for Fast Imaging of Wavelet Transforms.- Multiresolution Approach to Wavelets in Computer Vision.- Index of Contributors.

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書名 Wavelets : time-frequency methods and phase space : proceedings of the international conference, Marseille, France, December 14-18, 1987
著作者等 Combes, J. M.
Grossmann, A.
Tchamitchian, Philippe
Grossmann Alexander
Combes Jean-Michel
シリーズ名 Inverse problems and theoretical imaging
出版元 Springer-Verlag
刊行年月 c1990
版表示 2nd ed
ページ数 ix, 331 p.
大きさ 25 cm
ISBN 0387530142
NCID BA11467730
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言語 英語
出版国 ドイツ