Eric Malm
Harvey Mudd College Mathematics 2005
Thesis Proposal: | Decimation-in-Frequency Fast Fourier Transforms for the Symmetric Group |
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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 S_{n}
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 S_{n} 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.