http://web.mit.edu/18.327 http://web.mit.edu/1.130
18.327 and 1.130 COURSE ON WAVELETS, FILTER BANKS AND APPLICATIONS
Gilbert Strang (Math.) 
Kevin Amaratunga (Civil & Env. Eng.) 
gs@math.mit.edu 
kevina@mit.edu 
MONWED 1:303 in 1390 : Graduate (H) credit.
Text: WAVELETS AND FILTER BANKS by Strang and Nguyen, WellesleyCambridge
Press (1997)
Course structure: The course will consist of lectures, homework
assignments and a project on a topic related to the student's area of interest.
We will aim for the right balance of theory and **applications**. The course
has no specific prerequisites, although a basic knowledge of Fourier transforms
is recommended. We start with timeinvariant filters and basic wavelets.
The text gives an overall perspective of the field  which has grown with
amazing speed. The topics will include

Analysis of Filter Banks and Wavelets

Design Methods


Applications

Handson Experience with Software

These four key areas will be developed in detail:

Analysis. Multirate Signal Processing: Filtering, Decimation,
Polyphase, Perfect Reconstruction and Aliasing Removal. Matrix Analysis:
Toeplitz Matrices and Fast Algorithms. Wavelet Transform: Pyramid
and Cascade Algorithms, Daubechies Wavelets, Orthogonal and Biorthogonal
Wavelets, Smoothness, Approximation, Boundary Filters and Wavelets, TimeFrequency
and TimeScale Analysis, SecondGeneration Wavelets.

Design Methods. Spectral Factorization, CosineModulated Filter
Banks, Lattice Structure, Ladder Structure (Lifting.)

Applications. Audio and Image Compression, Quantization Effects,
Digital Communication and Multicarrier Modulation, Transmultiplexers, TextImage
Compression: Lossy and Lossless, Medical Imaging and Scientific Visualization,
Edge Detection and Feature Extraction, Seismic Signal Analysis, Geometric
Modeling, Matrix Preconditioning, Multiscale Methods for Partial Differential Equations and Integral Equations.

Simulation Software. MATLAB Wavelet Toolbox, Software for Filter Design, Signal Analysis, Image Compression, PDEs, Wavelet Transforms on Complex Geometrical Shapes.
We encourage you to learn about wavelets and their applications.
Multiresolution representation of a complex shape 