Wavelets

1. Front Matter

   Pages I-IX

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2. Introduction to Wavelet Transforms

   1. Front Matter

      Pages 1-1

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   2. Reading and Understanding Continuous Wavelet Transforms

      • A. Grossmann, R. Kronland-Martinet, J. Morlet

      Pages 2-20

   3. Orthonormal Wavelets

      • Y. Meyer

      Pages 21-37

   4. Orthonormal Bases of Wavelets with Finite Support — Connection with Discrete Filters

      • I. Daubechies

      Pages 38-66

3. Some Topics in Signal Analysis

   1. Front Matter

      Pages 67-67

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   2. Some Aspects of Non-Stationary Signal Processing with Emphasis on Time-Frequency and Time-Scale Methods

      • P. Flandrin

      Pages 68-98

   3. Detection of Abrupt Changes in Signal Processing

      • M. Basseville

      Pages 99-101

   4. The Computer, Music, and Sound Models

      • J.-C. Risset

      Pages 102-123

4. Wavelets and Signal Processing

   1. Front Matter

      Pages 125-125

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   2. Wavelets and Seismic Interpretation

      • J. L. Larsonneur, J. Morlet

      Pages 126-131

   3. Wavelet Transformations in Signal Detection

      • F. B. Tuteur

      Pages 132-138

   4. Use of Wavelet Transforms in the Study of Propagation of Transient Acoustic Signals Across a Plane Interface Between Two Homogeneous Media

      • S. Ginette, A. Grossmann, Ph. Tchamitchian

      Pages 139-146

   5. Time-Frequency Analysis of Signals Related to Scattering Problems in Acoustics Part I: Wigner-Ville Analysis of Echoes Scattered by a Spherical Shell

      • J. P. Sessarego, J. Sageloli, P. Flandrin, M. Zakharia

      Pages 147-153

   6. Coherence and Projectors in Acoustics

      • J. G. Slama

      Pages 154-157

   7. Wavelets and Granular Analysis of Speech

      • J. S. Liénard, C. d’Alessandro

      Pages 158-163

   8. Time-Frequency Representations of Broad-Band Signals

      • J. Bertrand, P. Bertrand

      Pages 164-171

   9. Operator Groups and Ambiguity Functions in Signal Processing

      • A. Berthon

      Pages 172-180

5. Mathematics and Mathematical Physics

   1. Front Matter

      Pages 181-181

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   2. Wavelet Transform Analysis of Invariant Measures of Some Dynamical Systems

      • A. Arneodo, G. Grasseau, M. Holschneider

      Pages 182-196

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.

• Algebra
• algorithms
• calculus
• differential equation
• dynamical systems
• fourier analysis
• operator
• partial differential equation
• phase
• signal
• signal analysis
• signal processing
• transformation
• wavelet
• wavelet transform

• Centre National de la Recherche Scientifique, Marseille Cedex 9, France

  Jean-Michel Combes, Alexander Grossmann, Philippe Tchamitchian

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