On the diagonalization of the discrete Fourier transform
type: Item
instance of: scholarly article
title: On the diagonalization of the discrete Fourier transform
zbMATH Open document ID: 1165.65089
author: Shamgar Gurevich
author: Ronny Hadani
published in: Applied and Computational Harmonic Analysis
publication date: 2009-06-25T00:00:00Z
review text: The authors describe a representation theoretic approach to the diagonalization problem of the discrete Fourier transform of length \(p\), where \(p>2\) is a prime number. Starting with the Weil representation of the finite symplectic group, the theory of tori in the one-dimensional Weil representation is discussed. Using a relation between the DFT and the Weil representation, a canonical basis \(\Phi\) of eigenvectors for the DFT is presented. The transition matrix \(\Theta\) from the standard basis to \(\Phi\) defines a novel transform, the so-called discrete oscillator transform. Finally, a fast algorithm for computing \(\Theta\) in certain cases is described.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 5570586
zbMATH Keywords: discrete Fourier transform
zbMATH Keywords: diagonalization
zbMATH Keywords: Weil representation
zbMATH Keywords: canonical eigenvectors
zbMATH Keywords: discrete oscillator transform
zbMATH Keywords: fast oscillator transform
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Heisenberg representation
zbMATH Keywords: finite symplectic group
zbMATH Keywords: transition matrix
Wikidata QID: Q56047063
MaRDI profile type: Publication
full work available at URL: j.acha.2008.11.003
OpenAlex ID: W2962743293
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DOI: 10.1016/J.ACHA.2008.11.003
description: scientific article; zbMATH DE number 5570586