Winter Term, 1999
WAVELETS AND APPLICATIONS
analysis scaling function synthesis
Time: TuTh 2:00-3:50, 104 Bradley
and Filter Banks" by G.
Strang and T. Nguyen, Wellesley-Cambridge
Topics to be discussed in class:
- Filters. Filtering, Shannon Sampling, Ideal
Filters, Time, Frequency, and Scale, Decimation, Polyphase, Perfect Reconstruction,
M-channel Filter Banks, Wavelets as Iterated Filter Banks, Pyramid Algorithm.
- Wavelets. Multiresolution Analysis, Bases
and Frames, Scaling Functions and Dilation Equations, Orthogonal and Biorthogonal
Wavelets, Accuracy of Approximation, Cascade Algorithm, Smoothness of Scaling
Functions, Fast Wavelet Transform, Multiwavelets.
- Design Methods. Paraunitary Matrices, Halfband
Filters, Spectral Factorization, Cosine-Modulated Filter Banks, Lattice
- Applications. Audio and Image Compression, Noise
Removal, Edge Detection and Feature Extraction, Refinement Methods for
Differential Equations, Your Own Application.
The course will include a project related to the
student's area of interest. There are no exams.
For more information contact the instructor at firstname.lastname@example.org
or visit http://math.dartmouth.edu/~m123w99