A Family of Matrices for Generating Hermite-Gaussian-Like DFT Eigenvectors

José R. de Oliveira Neto; Juliano B. Lima; Daniel Panario

ICASSP 2018accepted0 citations

A Family of Matrices for Generating Hermite-Gaussian-Like DFT Eigenvectors

José R. de Oliveira Neto, Juliano B. Lima, Daniel Panario

Abstract

A generating matrix is a matrix such that, when multiplied by an eigenvector of a discrete transform, a new eigenvector is obtained. In this paper, we introduce a family of generating matrices of DFT eigenvectors. We demonstrate that, if a specific initial set of eigenvectors is chosen, using the referred family of matrices, a Hermite-Gaussian-like DFT eigenbasis is obtained. Such an eigenbasis is then employed to define a discrete fractional Fourier transform which numerically approximates the corresponding continuous transform.

BibTeX

@inproceedings{icassp2018_afamilyofmatrice,
  title = {A Family of Matrices for Generating Hermite-Gaussian-Like DFT Eigenvectors},
  author = {José R. de Oliveira Neto and Juliano B. Lima and Daniel Panario},
  booktitle = {ICASSP 2018},
  year = {2018}
}