The discrete Fourier transform: A canonical basis of eigenfunctions
Information Theory
2008-08-26 v1 Discrete Mathematics
math.IT
Representation Theory
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.
Keywords
Cite
@article{arxiv.0808.3214,
title = {The discrete Fourier transform: A canonical basis of eigenfunctions},
author = {Shamgar Gurevich and Ronny Hadani and Nir Sochen},
journal= {arXiv preprint arXiv:0808.3214},
year = {2008}
}
Comments
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