High-accuracy centered fractional fourier transform matrix for optical imaging and other applications
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Apr 29, 2014
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Aug 5, 2013
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Nov 15, 2009
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Abstract
Methods for numerically generating a centered discrete fractional Fourier transform matrix on a computer, the centered discrete fractional Fourier transform matrix of size N by N where N is an odd integer. Centering is obtained by simple barrel roll operations on eigenvectors. High-accuracy is obtained by numerically calculating the eigenvectors of the discrete fractional Fourier transform matrix from a closed-form mathematical formula and then iteratively performing a Gram-Schmidt orthogonalization procedure until a resulting set of improved-orthogonal eigenvectors is produced that is sufficiently orthogonal.
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