This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris.
- Provides a broad perspective on the principles and applications of transient signal processing with wavelets.
- Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms.
- Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements.
- Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet.
- Content is accessible on several level of complexity, depending on the individual reader's needs.
- Reviews Fourier analysis and elementary signal processing.
- Introduces windowed Fourier transforms, continuous wavelet transforms, and Wigner-Ville transforms.
- Explains the construction of frames, wavelet orthogonal and biorthogonal bases, wavelet packet and local cosine bases.
- Covers basic approximation theory with applications to signal estimation and transform coding.