Computational Signal Processing with Wavelets - Anthony Teolis

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Sommaire:
1 Introduction.- 1.1 Motivation and Objectives.- 1.2 Core Material and Development.- 1.3 Hybrid Media Components.- 1.4 Signal Processing Perspective.- 2 Mathematical Preliminaries.- 2.1 Basic Symbols and Notation.- 2.2 Basic Concepts.- 2.3 Basic Spaces.- 2.4 Operators.- 2.5 Bases and Completeness in Hilbert Space.- 2.6 Fourier Transforms.- 2.7 Linear Filters.- 2.8 Analog Signals and Discretization.- Problems.- 3 Signal Representation and Frames.- 3.1 Inner Product Representation (Atomic Decomposition).- 3.2 Orthonormal Bases.- 3.3 Riesz Bases.- 3.4 General Frames.- Problems.- 4 Continuous Wavelet and Gabor Transforms.- 4.1 What Is a Wavelet?.- 4.2 Example Wavelets.- 4.3 Continuous Wavelet Transform.- 4.4 Inverse Wavelet Transform.- 4.5 Continuous Gabor Transform.- 4.6 Unified Representation and Groups.- Problems.- 5 Discrete Wavelet Transform.- 5.1 Discretization of the CWT.- 5.2 Multiresolution Analysis.- 5.3 Multiresolution Representation.- 5.4 Orthonormal Wavelet Bases.- 5.5 Compactly Supported (Daubechies) Wavelets.- 5.6 Fast Wavelet Transform Algorithm.- Problems.- 6 Overcomplete Wavelet Transform.- 6.1 Discretization of the CWT Revisited.- 6.2 Filter Bank Implementation.- 6.3 Time-Frequency Localization and Wavelet Design.- 6.4 OCWT Examples.- 6.5 Irregular Sampling and Frames.- Problems.- 7 Wavelet Signal Processing.- 7.1 Noise Suppression.- 7.2 Compression.- 7.3 Digital Communication.- 7.4 Identification.- 7.5 Conclusion.- Problems.- 8 Object-Oriented Wavelet Analysis with MATLAB 5.- 8.1 Wavelet Signal Processing Workstation.- 8.2 MATLAB Coding.- 8.3 The sampled_signal Object.- 8.4 Wavelet Transform Implementation.- 8.5 The wavelet Object.- 8.6 Processing Example.- 8.7 Supporting Functions and Globals.- References.