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

Author

Hanna, Magdy Tawfik ; Seif, Nabila Philip Attalla ; Ahmed, Waleed Abd El Maguid

Author_Institution

Dept. of Eng. Math. & Phys., Fayoum Univ.

Volume

54

Issue

7

fYear

2006

fDate

7/1/2006 12:00:00 AM

Firstpage

2815

Lastpage

2819

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

Keywords

Gaussian processes; eigenvalues and eigenfunctions; singular value decomposition; Gram-Schmidt algorithms; Hermite-Gaussian-like eigenvectors; discrete Fourier transform matrix; eigenspaces; orthogonal projection matrix; sequential orthogonal procrustes algorithm; singular value decomposition; Difference equations; Differential equations; Discrete Fourier transforms; Eigenvalues and eigenfunctions; Fourier transforms; Mathematics; Matrix decomposition; Physics; Singular value decomposition; Symmetric matrices; Discrete fractional Fourier transform; Gram–Schmidt algorithm (GSA); Hermite–Gaussian-like orthonormal eigenvectors; orthogonal procrustes algorithm (OPA); projection matrices; sequential orthogonal procrustes algorithm (SOPA);

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2006.873497

Filename

1643920