Application of the Weil representation: diagonalization of the discrete Fourier transform

Details Application of the Weil representation: diagonalization of the discrete Fourier transform Application of the Weil representation: diagonalization of the discrete Fourier transform

2009-02-04

arxiv.org/abs/0902.0668v1

Computer Science

Information Theory

To appear in the Proceedings of the Sixth Workshop on Lie Theory and Geometry, Cordoba, November 13 - 17, 2007 (Editors: C. S.

Scientific paper

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.

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