Wavelets

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