Coefficient-truncated higher-order commuting matrices of the discrete fourier transform
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(h2k) NtimesN DFT-commuting matrices proposed by Candan is restricted by 2k+1lesN. 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.