The discrete Fourier transform: A canonical basis of eigenfunctions

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dc.creatorGurevich, Shamgar
dc.creatorHadani, Ronny
dc.creatorSochen, Nir
dc.date2008-08-23
dc.date.accessioned2026-07-07T09:58:09Z
dc.date.available2026-07-07T09:58:09Z
dc.descriptionThe discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors for the 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). Finally, we describe a fast algorithm for computing the DOT in certain cases.
dc.descriptionTo appear in the proceeding of the 2008 European Signal Processing Conference (EUSIPCO-2008), Lausanne, Switzerland; MSC classifications: Fourier transform, Weil representation, symmetries, eigenfunctions, oscillator transform, fast oscillator transform
dc.identifierhttps://arxiv.org/abs/0808.3214
dc.identifierhttp://arxiv.org/abs/0808.3214
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167612
dc.subjectInformation Theory
dc.subjectDiscrete Mathematics
dc.subjectRepresentation Theory
dc.titleThe discrete Fourier transform: A canonical basis of eigenfunctions
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