Wavelets: A Mathematical Tool for Signal Analysis

Foreword Preface Software Notation 1. What are wavelets? Waveform modeling and segmentation Time-frequency analysis Fast algorithms and filter banks 2. Time-Frequency Localization. Analog filters RMS bandwidths The short-time Fourier transform The integral wavelet transform Modeling the cochlea 3. Multiresolution Analysis. Signal spaces with finite RMS bandwidth Two simple mathematical representations Multiresolution analysis Cardinal splines 4. Orthonormal Wavelets. Orthogonal wavelet spaces Wavelets of Haar, Shannon, and Meyer Spline wavelets of Battle-Lemarie and Stromberg The Daubechies wavelets 5. Biorthogonal Wavelets. The need for duals Compactly supported spline wavelets The duality principle Total positivity and optimality of time-frequency windows 6. Algorithms. Signal representations Orthogonal decompositions and reconstructions Graphical display of signal representations Multidimensional wavelet transforms The need for boundary wavelets Spline functions on a bounded interval Boundary spline wavelets with arbitrary knots 7. Applications. Detection of singularities and feature extraction Data compression Numerical solutions of integral equations Summary and Notes References Subject Index.

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