Eric Malm
Harvey Mudd College Mathematics 2005
| Thesis Proposal: | Decimation-in-Frequency Fast Fourier Transforms for the Symmetric Group |
|---|---|
| Problem Statement: | Decimation-in-Frequency FFTs for the Symmetric Group |
| Thesis Advisor: | Prof. Michael E. Orrison |
| Second Reader: | Prof. Shahriar Shahriari |
| E-Mail: | emalm[at]math.hmc.edu |
| Presentations: | 10-Minute Thesis Presentation |
| 20-Minute Thesis Presentation | |
| Atlanta Presentation: DIF FFTs for the Symmetric Group | |
| Admitted Students Program | |
| Presentation Days Slides | |
| Presentation Days Poster | |
| Documents: | |
| Bibliography: | emalm-2005-annbib.pdf |
| Expository Paper (Draft): | Recent Results in Generalized FFTs |
| Midyear Report: | emalm-2005-midyear.pdf |
| Thesis: | emalm-2005-thesis.pdf |
Decimation-in-Frequency Fast Fourier Transforms for Sn
The discrete Fourier transform provides a way to convert samples of a periodic function into frequency information about that function, and consequently underlies much of modern signal processing theory. In recent years, significant attention has been paid to group-theoretic generalizations of the discrete Fourier transform and to their efficient implementation. Much of the current research in generalized fast Fourier transforms for the symmetric group Sn has focused on separation of variables (decimation-in-time) algorithms. I intend to investigate projection-based (decimation-in-frquency) algorithms for the symmetric group, which may simplify both the theoretical framework for such FFTs and how such FFTs are implemented.