Fourier Transform Algorithm Research Paper

I wrote this paper as a part of the 2018 UChicago Math Summer Research Experience for Undergraduates (REU). The describes some of the theory behind Fourier analysis, and the Fourier transform for functions on finite groups. It focuses on an algorithm developed by Diaconis and Rockmore, which is a generalization of the classic Cooley-Tukey FFT algorithm. The paper provides a novel implementation of this algorithm using SageMath, and includes a run-time analysis as well. It also discusses applications of this type of Fourier transform for object tracking.