Title :
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.
fDate :
7/1/2006 12:00:00 AM
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);
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2006.873497
