Wavelets

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–Lemarié and Strömberg; 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.