Wavelets

Time-Frequency Methods and Phase Space

ISBN: 978-3-642-97179-2 (Print) 978-3-642-97177-8 (Online)

Table of contents (30 chapters)

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  1. Front Matter

    Pages I-IX

  2. Introduction to Wavelet Transforms

    1. Front Matter

      Pages 1-1

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      Chapter

      Pages 2-20

      Reading and Understanding Continuous Wavelet Transforms

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      Chapter

      Pages 21-37

      Orthonormal Wavelets

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      Chapter

      Pages 38-66

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

  3. Some Topics in Signal Analysis

    1. Front Matter

      Pages 67-67

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      Chapter

      Pages 68-98

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

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      Chapter

      Pages 99-101

      Detection of Abrupt Changes in Signal Processing

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      Chapter

      Pages 102-123

      The Computer, Music, and Sound Models

  4. Wavelets and Signal Processing

    1. Front Matter

      Pages 125-125

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      Chapter

      Pages 126-131

      Wavelets and Seismic Interpretation

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      Chapter

      Pages 132-138

      Wavelet Transformations in Signal Detection

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      Chapter

      Pages 139-146

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

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      Chapter

      Pages 147-153

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

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      Chapter

      Pages 154-157

      Coherence and Projectors in Acoustics

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      Chapter

      Pages 158-163

      Wavelets and Granular Analysis of Speech

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      Chapter

      Pages 164-171

      Time-Frequency Representations of Broad-Band Signals

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      Chapter

      Pages 172-180

      Operator Groups and Ambiguity Functions in Signal Processing

  5. Mathematics and Mathematical Physics

    1. Front Matter

      Pages 181-181

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      Chapter

      Pages 182-196

      Wavelet Transform Analysis of Invariant Measures of Some Dynamical Systems

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      Chapter

      Pages 197-203

      Holomorphic Integral Representations for the Solutions of the Helmholtz Equation

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      Chapter

      Pages 204-208

      Wavelets and Path Integral

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      Chapter

      Pages 209-215

      Mean Value Theorems and Concentration Operators in Bargmann and Bergman Space

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      Chapter

      Pages 216-220

      Besov Sobolev Algebras of Symbols

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      Chapter

      Pages 221-231

      Poincaré Coherent States and Relativistic Phase Space Analysis

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