Coefficient-truncated higher-order commuting matrices of the discrete Fourier transform
Journal
IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
Pages
3545-3548
Date Issued
2008-04
Author(s)
Abstract
Recently, Candan introduced higher order DFT-commuting matrices whose eigenvectors are accurate approximations to the continuous Hermite-Gaussian functions (HGFs). However, the highest order 2k of the O(h 2k ) N×N DFT-commuting matrices proposed by Candan is restricted by 2k+1≤N. In this paper, we remove that restriction of order upper bound by developing a coefficient truncation technique to construct arbitrary-order DFT-commuting matrices. Exploiting that coefficient truncation technique, we also develop a method to construct n-diagonal arbitrary-order DFT-commuting matrices, whose number of nonzero diagonal bands n can be prespecified at will. Results of computer experiments show that the Hermite-Gaussian-like (HGL) eigenvectors of the new DFT-commuting matrices proposed in this paper outperform those of Candan’s.
Type
conference paper