The discrete Fourier transform: A canonical basis of eigenfunctions

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The 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.
To 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

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Information Theory, Discrete Mathematics, Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/167612

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.3214
 http://arxiv.org/abs/0808.3214

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arXiv