San Francisco State University

Math 490.1

Introduction to Wavelets, Frames and Applications

Spring, 2014, Tu 17:10 - 19:50, Room: TH 211

Instructor: Dr. Shidong Li

Syllabus and class schedule

Course description: wavelets and frames are relatively new and fast developing subjects in mathematics. They are tools for function/signal analysis in a form of a basis or an overcomplete system in a space. Although some of the topics have only been recently formalized, wavelets and frames have deep roots in physics and engineering applications. They plays an extremely useful role in applications such as acoustic and seismic signal processing, signal/image compression and time-frequency analysis of sophisticated signals. This class will provide an introduction to the theory of wavelets and frames, and demonstrate how modern mathematics is integrated with engineering and physics applications. The class is designed to be accessible to higher level undergraduate students and graduate students who have had Math 325 (Linear Algebra) or with the consent of the instructor. Students who are interested in taking the class are strongly encouraged to talk to Dr. Shidong Li.

Starting with some review of linear algebra, the class will include the fundamentals of theories of wavelets, frames, Gabor frames, and their applications to engineering and physics, particularly to topics of signal processing. Projects will be an integrated components of the course. These projects are designed for the understanding of the theory, applications to real life problems and design of your own wavelets/frames.

Reading Material and Software Tool:

Frames for undergraduates, by Deguang Han, etc.

An Introduction to Wavelets Through Linear Algebra, by Michael Frazier

Lecture Notes

Matlab Wavelet Toolbox (Software, limited use provided)

For syllabus and more information about the class or wavelet/frame related subjects, please contact Dr. Shidong Li.

Wavelet Class Syllabus (tentative)
Project Data Set (shift + click)