Computational Signal Processing with Wavelets (eBook, PDF) - Teolis, Anthony
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1 Introduction1.1 Motivation and Objectives1.2 Core Material and Development1.3 Hybrid Media Components1.4 Signal Processing Perspective1.4.1 Analog Signals1.4.2 Digital Processing of Analog Signals1.4.3 Time-Frequency Limitedness 2 Mathematical Preliminaries2.1 Basic Symbols and Notation2.2 Basic Concepts2.2.1 Norm2.2.2 Inner Product2.2.3 Convergence2.2.4 Hilbert Spaces2.3 Basic Spaces2.3.1 Bounded Functions2.3.2 Absolutely Integrable Functions2.3.3 Finite Energy Functions2.3.4 Finite Energy Periodic Functions2.3.5 Time-Frequency Concentrated Functions2.3.6 Finite Energy Sequences2.3.7 Bandlimited Functions2.3.8 Hardy Spaces2.4 Operators2.4.1 Bounded Linear Operators2.4.2 Properties2.4.3 Useful Unitary Operators2.5 Bases and Completeness in Hilbert Space2.6 Fourier Transforms2.6.1 Continuous Time Fourier Transform2.6.2 Continuous Time-Periodic Fourier Transform2.6.3 Discrete Time Fourier Transform2.6.4 Discrete Fourier Transform2.6.5 Fourier Dual Spaces2.7 Linear Filters2.7.1 Continuous Filters and Fourier Transforms2.7.2 Discrete Filters and Z-Transforms2.8 Analog Signals and Discretization2.8.1 Classical Sampling Theorem2.8.2 What Can Be Computed Exactly?Problems 3 Signal Representation and Frames3.1 Inner Product Representation (Atomic Decomposition)3.2 Orthonormal Bases3.2.1 Parseval and Plancherel3.2.2 Reconstruction3.2.3 Examples3.3 Riesz Bases3.3.1 Reconstruction3.3.2 Examples3.4 General Frames3.4.1 Basic Frame Theory3.4.2 Frame Representation3.4.3 Frame Correlation and Pseudo-Inverse3.4.4 Pseudo-Inverse3.4.5 Best Frame Bounds3.4.6 Duality3.4.7 Iterative ReconstructionProblems 4 Continuous Wavelet and Gabor Transforms4.1 What is a Wavelet?4.2 Example Wavelets4.2.1 Haar Wavelet4.2.2 Shannon Wavelet4.2.3 Frequency B-spline Wavelets4.2.4 Morlet Wavelet4.2.5 Time-Frequency Tradeoffs4.3 Continuous Wavelet Transform4.3.1 Definition4.3.2 Properties4.4 Inverse Wavelet Transform4.4.1 The Idea Behind the Inverse4.4.2 Derivation for L 2 ( R )4.4.3 Analytic Signals4.4.4 Admissibility4.5 Continuous Gabor Transform4.5.1 Definition4.5.2 Inverse Gabor Transform4.6 Unified Representation and Groups4.6.1 Groups4.6.2 Weighted Spaces4.6.3 Representation4.6.4 Reproducing Kernel4.6.5 Group Representation TransformProblems 5 Discrete Wavelet Transform5.1 Discretization of the CWT5.2 Multiresolution Analysis5.2.1 Multiresolution Design5.2.2 Resolution and Dilation Invariance5.2.3 Definition5.3 Multiresolution Representation5.3.1 Projection5.3.2 Fourier Transforms5.3.3 Between Scale Relations5.3.4 Haar MRA5.4 Orthonormal Wavelet Bases5.4.1 Characterizing W 05.4.2 Wavelet Construction5.4.3 The Scaling Function5.5 Compactly Supported (Daubechies) Wavelets5.5.1 Main Idea5.5.2 T

Introduction.- Mathematical Preliminaries.- Signal Representation and Frames.- Continuous Wavelet and Gabor Transforms.- Discrete Wavelet Transform.- Overcomplete Wavelet Transform.- Wavelet Signal Processing.- Object-Oriented Wavelet Analysis with MATLAB 5.- References.- Index.
"This book provides an expository treatment of wavelets from a signal processing perspective. The focus is on the expansion of signals in overcomplete wavelet systems. All illustrations of the theory are generated in the framework of the Matlab toolbox wavelet signal processing workstation (WSPW) made publicly available by the author.... The last chapter is a manual for WSPW, and the whole book serves as an extended manual." -Mathematical Reviews "This book provides a bridge between theory and practice of wavelet-based signal processing and is written for both students and professionals. A solid mathematical foundation is given in the beginning chapters [1-6].... Several applications of wavelet-based signal processing including noise suppression, signal compression, signal identification and digital communication are presented in Chapter 7. Chapter 8 gives numerical illustrations and examples of wavelet methods using MATLAB 5. The accomanying MATLAB-based software is available on the world wide web. Every chapter of the book contains a collection of exercises." -Zentralblatt MATH "A self-contained text that is theoretically rigorous while maintaining contact with interesting applications. A particularly noteworthy a class of 'overcomplete wavelets'. These functions are not orthonormal and they lead to many useful results." -Journal of Mathematical Psychology