A discrete fractional Fourier transform based on orthonormalized McClellan-Parks eigenvectors

A version of the discrete fractional Fourier transform (DFRFT) is developed with the objective of approximating the continuous fractional Fourier transform (FRFT). First the McClellan-Parks nonorthogonal eigenvectors of the discrete Fourier transform (DFT) matrix are generated analytically after deriving explicit expressions for the elements of those vectors. Second the Gram-Schmidt technique is applied to orthonormalize the eigenvectors in each eigensubspace individually. Third Hermite-like approximate eigenvectors are generated. Finally exact orthonormal eigenvectors as close as possible to the Hermite-like approximate eigenvectors are obtained by the orthogonal procrustes algorithm.