Eric Malm

Harvey Mudd College Mathematics 2005

mugshot
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.

\n