2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218484We 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.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 transformInformation TheoryDiscrete MathematicsRepresentation Theorytext