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| Preface | |
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| Acknowledgments | |
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| The Complex Plane and the Space L<sup>2</sup>(R) | |
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| Complex Numbers and Basic Operations | |
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| Problems | |
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| The Space L<sup>2</sup>(R) | |
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| Problems | |
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| Inner Products | |
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| Problems | |
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| Bases and Projections | |
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| Problems | |
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| Fourier Series and Fourier Transformations | |
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| Euler's Formula and the Complex Exponential Function | |
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| Problems | |
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| Fourier Series | |
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| Problems | |
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| The Fourier Transform | |
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| Problems | |
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| Convolution and B-Splines | |
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| Problems | |
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| Haar Spaces | |
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| The Haar Space V<sub>0</sub> | |
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| Problems | |
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| The General Haar Space V<sub>j</sub> | |
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| Problems | |
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| The Haar Wavelet Space W<sub>0</sub> | |
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| Problems | |
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| The General Haar Wavelet Space W<sub>j</sub> | |
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| Problems | |
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| Decomposition and Reconstruction | |
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| Problems | |
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| Summary | |
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| The Discrete Haar Wavelet Transform and Applications | |
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| The One-Dimensional Transform | |
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| Problems | |
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| The Two-Dimensional Transform | |
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| Problems | |
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| Edge Detection and Naive Image Compression | |
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| Multiresolution Analysis | |
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| Multiresolution Analysis | |
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| Problems | |
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| The View from the Transform Domain | |
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| Problems | |
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| Examples of Multiresolution Analyses | |
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| Problems | |
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| Summary | |
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| Daubechies Scaling Functions and Wavelets | |
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| Constructing the Daubechies Scaling Functions | |
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| Problems | |
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| The Cascade Algorithm | |
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| Problems | |
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| Orthogonal Translates, Coding, and Projections | |
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| Problems | |
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| The Discrete Daubechies Transformation and Applications | |
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| The Discrete Daubechies Wavelet Transform | |
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| Problems | |
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| Projections and Signal and Image Compression | |
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| Problems | |
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| Naive Image Segmentation | |
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| Problems | |
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| Biorthogonal Scaling Functions and Wavelets | |
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| A Biorthogonal Example and Duality | |
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| Problems | |
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| Biorthogonality Conditions for Symbols and Wavelet Spaces | |
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| Problems | |
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| Biorthogonal Spline Filter Pairs and the CDF97 Filter Pair | |
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| Problems | |
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| Decomposition and Reconstruction | |
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| Problems | |
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| The Discrete Biorthogonal Wavelet Transform | |
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| Problems | |
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| Riesz Basis Theory | |
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| Problems | |
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| Wavelet Packets | |
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| Constructing Wavelet Packet Functions | |
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| Problems | |
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| Wavelet Packet Spaces | |
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| Problems | |
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| The Discrete Packet Transform and Best Basis Algorithm | |
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| Problems | |
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| The FBI Fingerprint Compression Standard | |
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| Huffman Coding | |
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| Problems | |
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| References | |
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| Topic Index | |
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| Author Index | |