Sara E. Gussin

Harvey Mudd College Mathematics 2008

Thesis Proposal: Multidimensional Wavelet Analysis
10-Minute Presentation: 10-Minute Presentation
20-Minute Presentation: 20-Minute Presentation
Poster: Wavelet Sets
Final Presentation: Final Presentation
Final Report: Wavelets and Wavelet Sets

Thesis Advisor: Prof. Jon Jacobsen
Second Reader: Prof. Darryl Yong

Wavelets and Wavelet Sets

Wavelets are functions that are useful for representing signals and approximating other functions. Wavelet sets are defined in terms of Fourier transforms of certain wavelet functions. In this thesis, we provide an introduction to wavelets and wavelet sets, examine the pre-existing literature on the subject, and investigate an algorithm for creating wavelet sets. This algorithm (from The Construction of Single Wavelets in D-Dimensions by Benedetto and Leon) creates single wavelets, which can be used to create bases for L^2(R^n) through dilation and translation. We investigate the convergence properties of the algorithm, and implement it in Matlab.