On the diagonalization of the discrete Fourier transform
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 discrete oscillator transform in certain cases.
Keywords
Cite
@article{arxiv.0808.3281,
title = {On the diagonalization of the discrete Fourier transform},
author = {Shamgar Gurevich and Ronny Hadani},
journal= {arXiv preprint arXiv:0808.3281},
year = {2008}
}
Comments
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