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

Published 4 Feb 2009 in cs.IT, cs.DM, math.IT, and math.RT | (0902.0668v1)

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.

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