Instructor: David Walnut
Office: ST1, room 261
Phone: 703 993 1478 (voice)  703 993 1491 (fax)
email: dwalnut@gmu.edu

Office hours: By appointment.

Text: D. Walnut An Introduction to Wavelet Analysis, Birkhauser, Boston (2001), ISBN 0-8176-3962-4.

         K. Grochenig, Foundations of Time-Frequency Analysis, Birkhauser, Boston (2001), ISBN 0-8176-4022-3.

Prerequisites: MATH 315 or equivalent and computer literacy (we will use MATLAB). Some knowledge of Fourier Analysis and Functional Analysis is helpful but not required.

Topics: The goal of the course is to introduce the student to some of the basic concepts, constructions and applications of time-frequency decompositions including wavelet bases and Gabor frames. The schedule below may change as circumstances warrant.

• Week 1:  Review of Orthonormal Bases in Hilbert Spaces.
• Week 2:  Review of Fourier Analysis
• Week 3:  Wavelet Orthonormal Bases for L^2(R)
• Week 4:  Multiresolution Analysis
• Week 5:  Filter Banks and the Discrete Wavelet Transform
• Week 6:  Daubechies Wavelets
• Week 7:  Wavelet Packets and Best Bases
• Week 8:  Application: Image Compression and The BCR Algorithm
• Week 9:  Local Cosine Bases
• Week 10:  Nonorthogonal Bases and Frames in Hilbert Space
• Week 11:  Gabor Systems: Existence and Basic Properties
• Week 12:  Gabor Systems: Duality and Density
• Week 13:  The Zak Transform and the Balian-Low Theorem
• Week 14:  Project Presentations

Grading: The grade will be based on homework assignments, including some assignments using MATLAB, and on a semester project of the student's own choosing to be presented at the end of the semester. Details on the project will be made available.