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arXiv · 0808.3214

The discrete Fourier transform: A canonical basis of eigenfunctions

Shamgar Gurevich·Ronny Hadani·Nir Sochen
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Abstract

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.

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Shamgar Gurevich, Ronny Hadani, Nir Sochen. 2008-08-23. The discrete Fourier transform: A canonical basis of eigenfunctions. https://arxiv.org/abs/0808.3214

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