Hermite-Gaussian-like eigenvectors of the discrete Fourier transform matrix based on the direct utilization of the orthogonal projection matrices on its eigenspaces

Abstract

A new version is proposed for the Gram-Schmidt algorithm (GSA), the orthogonal procrustes algorithm (OPA) and the sequential orthogonal procrustes algorithm (SOPA) for generating Hermite-Gaussian-like orthonormal eigenvectors for the discrete Fourier transform matrix F. This version is based on the direct utilization of the orthogonal projection matrices on the eigenspaces of matrix F rather than the singular value decomposition of those matrices for the purpose of generating initial orthonormal eigenvectors. The proposed version of the algorithms has the merit of achieving a significant reduction in the computation time