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

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3 Author(s)
Hanna, M.T. ; Dept. of Eng. Math. & Phys., Fayoum Univ. ; Attalla Seif, N.P. ; Abd El Maguid Ahmed, M.W.

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

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Signal Processing, IEEE Transactions on  (Volume:54 ,  Issue: 7 )