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.