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| Preface | |
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| Acknowledgments | |
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| Prologue: Compression of the FBI Fingerprint Files | |
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| Background: Complex Numbers and Linear Algebra | |
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| Real Numbers and Complex Numbers | |
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| Complex Series, Euler's Formula, and the Roots of Unity | |
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| Vector Spaces and Bases | |
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| Linear Transformations, Matrices, and Change of Basis | |
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| Diagonalization of Linear Transformations and Matrices | |
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| Inner Products, Orthonormal Bases, and Unitary Matrices | |
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| The Discrete Fourier Transform | |
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| Basic Properties of the Discrete Fourier Transform | |
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| Translation-Invariant Linear Transformations | |
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| The Fast Fourier Transform | |
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| Wavelets on $bZ_N$ | |
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| Construction of Wavelets on $bZ_N$: The First Stage | |
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| Construction of Wavelets on $bZ_N$: The Iteration Step | |
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| Examples and Applications | |
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| Wavelets on $bZ$ | |
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| $ ell ^2(bZ)$ | |
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| Complete Orthonormal Sets in Hilbert Spaces | |
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| $L^2([- pi , pi ))$ and Fourier Series | |
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| The Fourier Transform and Convolution on $ ell ^2(bZ)$ | |
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| First-Stage Wavelets on $bZ$ | |
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| The Iteration Step for Wavelets on $bZ$ | |
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| Implementation and Examples | |
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| Wavelets on $bR$ | |
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| $L^2(bR)$ and Approximate Identities | |
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| The Fourier Transform on $bR$ | |
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| Multiresolution Analysis and Wavelets | |
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| Construction of Multiresolution Analyses | |
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| Wavelets with Compact Support and Their Computation | |
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| Wavelets and Differential Equations | |
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| The Condition Number of a Matrix | |
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| Finite Difference Methods for Differential Equations | |
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| Wavelet-Galerkin Methods for Differential Equations | |
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| Bibliography | |
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| Index | |