1. Wavelets, Filter Banks and Multiresolution Signal Processing. 1.1 Series Expansions of Signals. 1.2 Multiresolution Concept. 1.3 Overview of the Book.
2. Fundamentals of Signal Decompositions. 2.1 Notations. 2.2 Hilbert Spaces. 2.3 Elements of Linear Algebra. 2.4 Fourier Theory and Sampling. 2.5 Signal Processing. 2.6 Time-Frequency Representations. 2.A Bounded Linear Operators on Hilbert Spaces. 2.B Parametrization of Unitary Matrices. 2.C Convergence and Regularity of Functions.
3. Discrete-Time Bases and Filter Banks. 3.1 Series Expansions of Discrete-Time Signals. 3.2 Two- Channel Filter Banks. 3.3 Tree-Structured Filter Banks. 3.4 Multichannel Filter Banks. 3.5 Pyramids and Overcomplete Expansions. 3.6 Multidimensional Filter Banks. 3.7 Transmultiplexers and Adaptive Filtering in Subbands. 3.A Lossless Systems. 3.B Sampling in Multiple Dimensions and Multirate Operations.
4. Series Expansions using Wavelets and Modulated Bases. 4.1 Definition of the Problem. 4.2 Multiresolution Concept and Analysis. 4.3 Construction of Wavelets Using Fourier Techniques. 4.4 Wavelets Derived from Iterated Filter Banks and Regularity. 4.5 Wavelet Series and Its Properties. 4.6 Generalizations in One Dimension. 4.7 Multidimensional Wavelets. 4.8 Local Cosine Bases. 4.A Proof of Theorem.
5. Continuous Wavelet and Short-Time Fourier Transforms and Frames. 5.1 Continuous Wavelet Transform. 5.2 Continuous Short-Time Fourier Transform. 5.3 Frames of Wavelet and Short-Time Fourier Transforms.
6. Algorithms and Complexity. 6.1 Classic Results. 6.2 Complexity of Discrete Bases Computation. 6.3 Complexity of Wavelet Series Computation. 6.4 Complexity of Overcomplete Expansions. 6.5 Special Topics.
7. Signal Compression and Subband Coding. 7.1 Compression Systems Based on Linear Transforms. 7.2 Speech and Audio Compression. 7.3 Image Compression. 7.4 Video Compression. 7.5 Joint Source-Channel Coding. 7.A Statistical Signal Processing.
Bibliography. Index. 