Closed-form eigenvectors of the discrete Fourier Transform
Journal
Proceedings - IEEE International Symposium on Circuits and Systems
Pages
2597-2600
Date Issued
2013
Author(s)
Hsue, W.-L.
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 (k 2 N)-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.
Type
conference paper