Application of the Weil representation: diagonalization of the discrete Fourier transform
Information Theory
2009-02-05 v1 Discrete Mathematics
math.IT
Representation Theory
Abstract
We survey a new application of the Weil representation to construct a canonical basis of eigenvectors for the discrete Fourier transform (DFT). The transition matrix from the standard basis to the canonical basis defines a novel transform which we call the discrete oscillator transform (DOT for short). In addition, we describe a fast algorithm for computing the DOT in certain cases.
Keywords
Cite
@article{arxiv.0902.0668,
title = {Application of the Weil representation: diagonalization of the discrete Fourier transform},
author = {SHamgar Gurevich and Ronny Hadani},
journal= {arXiv preprint arXiv:0902.0668},
year = {2009}
}
Comments
To appear in the Proceedings of the Sixth Workshop on Lie Theory and Geometry, Cordoba, November 13 - 17, 2007 (Editors: C. S. Gordon, F. Grunewald, C. Olmos, J. A. Tirao, J. A. Wolf). Key word: Discrete Fourier transform; Weil representation; Canonical eigenvectors; Oscillator transform; Fast oscillator transform