DFT-commuting matrix with arbitrary or infinite order second derivative approximation

Authors:
Soo-Chang Pei;Wen-Liang Hsue;Jian-Jiun Ding
Affiliations:
Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan;Department of Electronics and Optoelectronics Application, Ian-Yang Institute of Technology, I-Ian, Taiwan;Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan
Venue:
IEEE Transactions on Signal Processing
Year:
2009

Citing 5
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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(h2k) N × N DFT-commuting matrices proposed by Candan is restricted by 2k + 1 ≤ 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 mfinite-order DFT -commuting matrix are shown to be the same as those of the n2 DFT -commuting matrix recently discovered in the literature.