Name
Title | ||
|---|---|---|
DFT-commuting matrix with arbitrary or infinite order second derivative approximation |
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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1109/TSP.2008.2007927 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
hgl eigenvectors,higher order,n dft-commuting,n2 dft,highest order,arbitrary-order dft-commuting matrix,new proposed dft,order upper bound restriction,better approximation,mfinite-order dft,derivative approximation,infinite order,function approximation,eigenvector,gaussian processes,hermitian matrices,fourier transforms,differential equations,eigenvectors,fractional fourier transform,indexing terms,discrete fourier transform,upper bound | Mathematical optimization,Combinatorics,Second derivative,Function approximation,Matrix (mathematics),Upper and lower bounds,Pure mathematics,Gaussian process,Discrete Fourier transform,Hermitian matrix,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
57 | 1 | 1053-587X |
Citations | PageRank | References |
6 | 0.69 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Soo-Chang Pei | 1 | 449 | 46.82 |
| Wen-Liang Hsue | 2 | 100 | 10.67 |
| Jian-Jiun Ding | 3 | 738 | 88.09 |