Contents
1 The Continuous Wavelet Transform
1.1 Definition and Elementary Properties
1.3 Filter Properties of the Wavelet Transform
1.3.1 Phase-Space Representations and Localization Operators
1.3.2 Wavelet Transform versus Windowed Fourier Transform
1.4.1 Asymptotic Behaviour in the Frequency Parameter
1.4.2 Remarks About the Order of Wavelets
1.6 Group-Theoretical Foundations and Generalizations
1.6.1 The Orthogonality Relation for Locally Compact Groups
1.6.2.1 The Wavelet Transform in L2(ℝ)
1.6.2.2 The Windowed Fourier Transform
1.6.2.3 The Wavelet Transform inn L2(ℝ)2
1.7 Extension of the One-Dimensional Wavelet Transform to Sobolev Spaces
2 The DiscreteWavelet Transform
2.1.1 Introduction and Definition
2.2.1 One-Dimensional Multiscale Analysis
2.2.2 Multidimensional Multiscale Analysis
2.4 One-Dimensional Orthogonal Wavelets
2.4.2 Solving Scaling Equations
2.4.3 Orthogonal Wavelets with Compact Support
2.4.4 Properties of the Daubechies Wavelets
2.4.6 Wavelets Adapted to Operators
2.4.6.1 Wavelet–Vaguelette Decompositions
2.4.6.2 Wavelet–Wavelet Decompositions
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