On the diagonalization of the discrete Fourier transform

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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 discrete oscillator transform in certain cases.
Accepted for publication in the journal "Applied and Computational Harmonic Analysis": Appl. Comput. Harmon. Anal. (2009), doi:10.1016/j.acha.2008.11.003. Key words: Discrete Fourier Transform, Weil Representation, Canonical Eigenvectors, Oscillator Transform, Fast Oscillator Transform

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Information Theory, Discrete Mathematics, Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/213542

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.3281
 http://arxiv.org/abs/0808.3281

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arXiv