18.327 and 1.130 COURSE ON WAVELETS, FILTER BANKS AND APPLICATIONS
MON-WED 1:30-3 in 1-390 : Graduate (H) credit.
|Gilbert Strang (Math.)
Kevin Amaratunga (Civil & Env. Eng.)
Text: WAVELETS AND FILTER BANKS by Strang and Nguyen, Wellesley-Cambridge
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 time-invariant 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
Hands-on Experience with Software
These four key areas will be developed in detail:
We encourage you to learn about wavelets and their applications.
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, Time-Frequency
and Time-Scale Analysis, Second-Generation Wavelets.
Design Methods. Spectral Factorization, Cosine-Modulated Filter
Banks, Lattice Structure, Ladder Structure (Lifting.)
Applications. Audio and Image Compression, Quantization Effects,
Digital Communication and Multicarrier Modulation, Transmultiplexers, Text-Image
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.
Multiresolution representation of a complex shape