1. Introduction; 2. Filters; 3. Downsampling and upsampling; 4. Filter banks; 5. Orthogonal filter banks; 6. Multiresolution; 7. Wavelet theory; 8. Finite length signals; 9. M-channel filter banks; 10. Design methods; 11. Applications; The discrete cosine transform; The lifting scheme; Block transforms in image coding.
Gilbert Strang received his Ph.D. from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. He is a Professor of Mathematics at MIT and an Honorary Fellow of Balliol College. Professor Strang has published eight textbooks. He received the von Neumann Medal of the US Association for Computational Mechanics, and the Henrici Prize for applied analysis. The first Su Buchin Prize from the International Congress of Industrial and Applied Mathematics, and the Haimo Prize from the Mathematical Association of America, were awarded for his contributions to teaching around the world. Truong Nguyen came to the Jacobs School in 2001. He manages the Video Processing Group, and teaches courses associated with the Signal Image Processing Program (SIP). He is a 1995 recipient of an NSF career award and is author of several MATLAB-based toolboxes on image compression, electrocardiogram compression, and filter bank design. He also holds a patent on an efficient design method for wavelets and filter banks and several patents on wavelet applications including compression and signal analysis. He received his Ph.D. from Caltech in 1989.