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| Introduction | |
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| Prerequisites | |
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| Guide to the Book | |
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| Background Information | |
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| A First Example | |
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| The Example | |
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| Generalizations | |
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| Exercises | |
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| The Discrete Wavelet Transform via Lifting | |
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| The First Example Again | |
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| De nition of Lifting | |
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| A Second Example | |
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| Lifting in General | |
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| DWT in General | |
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| Further Examples | |
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| Exercises | |
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| Analysis of Synthetic Signals | |
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| The Haar Transform | |
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| The CDF(2,2) Transform | |
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| Exercises | |
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| Interpretation | |
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| The First Example | |
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| Further Results on the Haar Transform | |
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| Interpretation of General DWT | |
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| Exercises | |
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| Two Dimensional Transforms | |
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| One Scale DWT in Two Dimensions | |
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| Interpretation and Examples | |
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| A 2D Transform Based on Lifting | |
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| Exercises | |
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| Lifting and Filters I | |
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| Fourier Series and the z-Transform | |
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| Lifting in the z-Transform Representation | |
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| Two Channel Filter Banks | |
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| Orthonormal and Biorthogonal Bases | |
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| Two Channel Filter Banks in the Time Domain | |
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| Summary of Results on Lifting and Filters | |
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| Properties of Orthogonal Filters | |
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| Some Examples | |
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| Exercises | |
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| Wavelet Packets | |
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| From Wavelets to Wavelet Packets | |
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| Choice of Basis | |
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| Cost Functions | |
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| Exercises | |
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| The Time-Frequency Plane | |
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| Sampling and Frequency Contents | |
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| De nition of the Time-Frequency Plane | |
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| Wavelet Packets and Frequency Contents | |
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| More about Time-Frequency Planes | |
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| More Fourier Analysis. The Spectrogram | |
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| Exercises | |
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| Finite Signals | |
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| The Extent of the Boundary Problem | |
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| DWT in Matrix Form | |
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| Gram-Schmidt Boundary Filters | |
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| Periodization | |
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| Moment Preserving Boundary Filters | |
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| Exercises | |
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| Implementation | |
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| Introduction to Software | |
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| Implementing the Haar Transform Through Lifting | |
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| Implementing the DWT Through Lifting | |
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| The Real Time Method | |
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| Filter Bank Implementation | |
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| Construction of Boundary Filters | |
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| Wavelet Packet Decomposition | |
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| Wavelet Packet Bases | |
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| Cost Functions | |
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| Exercises | |
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| Lifting and Filters II | |
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| The Three Basic Representations | |
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| From Matrix to Equation Form | |
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| From Equation to Filter Form | |
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| From Filters to Lifting Steps | |
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| Factoring Daubechies 4 into Lifting Steps | |
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| Factorizing Coi et 12 into Lifting Steps | |
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| Exercises | |
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| Wavelets in Matlab | |
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| Multiresolution Analysis | |
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| Frequency Properties of the Wavelet Transform | |
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| Wavelet Packets Used for Denoising | |
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| Best Basis Algorithm | |
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| Some Commands in Uvi Wave | |
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| Exercises | |
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| Applications and Outlook | |
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| Applications | |
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| Outlook | |
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| Some Web Sites | |
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| References | |
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| Index | |