2009/02/04 by Shamgar Gurevich, SHamgar Gurevich, Ronny Hadani +2
Computer Science · Mathematics · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Information Theory (cs.IT) #Representation Theory (math.RT) #cs.DM #cs.IT #math.IT #math.RT
paper · pdf · doi:10.48550/arxiv.0902.0668
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
arxiv created 2009/02/04 · openalex publication_date 2009/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.