DFT-commuting matrix with arbitrary or infinite-order second-derivative approximation
Journal
IEEE Transactions on Signal Processing
Journal Volume
57
Journal Issue
1
Pages
390-394
Date Issued
2009-01
Author(s)
Abstract
Recently, Candan introduced higher order DFT-commuting matrices whose eigenvectors are better approximations to the continuous Hermite-Gaussian functions (HGFs). However, the highest order 2k of the O(h 2k ) NtimesN DFT-commuting matrices proposed by Candan is restricted by 2k+1 les N. In this paper, we remove this order upper bound restriction by developing two methods to construct arbitrary-order DFT-commuting matrices. Computer experimental results show that the Hermite-Gaussian-like (HGL) eigenvectors of the new proposed DFT-commuting matrices outperform those of Candan. In addition, the HGL eigenvectors of the infinite-order DFT-commuting matrix are shown to be the same as those of the n 2 DFT-commuting matrix recently discovered in the literature.
Type
journal article