Name
Abstract | ||
|---|---|---|
Properties of eigenvectors and eigenvalues for discrete Fourier transform (DFT) are important for defining and understanding the discrete fractional Fourier transform (DFRFT). In this paper, we first propose a closed-form formula to construct an eigenvector of N-point DFT by down-sampling and then folding any eigenvector of (4N)-point DFT. The result is then generalized to derive eigenvectors of N-point DFT from eigenvectors of (k2N)-point DFT. To show an application of the proposed new closed-form DFT eigenvectors, Hermite-Gaussian-like (HGL) DFT eigenvectors which are much closer to the continuous Hermite-Gaussian functions (HGFs) are computed from existing HGL DFT eigenvectors of larger sizes with computer experiments. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/ISCAS.2013.6572410 | ISCAS |
Keywords | Field | DocType |
hermitian matrices,closed-form eigenvectors,discrete fourier transforms,hermite-gaussian-like,eigenvalues and eigenfunctions,discrete fractional fourier transform,vectors,tin,signal processing | Cyclotomic fast Fourier transform,Eigenvalue perturbation,Mathematical analysis,Eigenvalues and eigenvectors of the second derivative,Defective matrix,Discrete Fourier transform (general),Discrete Fourier transform,Discrete sine transform,Mathematics,DFT matrix | Conference |
ISSN | ISBN | Citations |
0271-4302 | 978-1-4673-5760-9 | 1 |
PageRank | References | Authors |
0.38 | 3 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wen-Liang Hsue | 1 | 100 | 10.67 |
| Soo-Chang Pei | 2 | 449 | 46.82 |