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Discrete and finite fractional Fourier transforms

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Abstract

Finite models for oscillator or waveguide systems provide corresponding fractional Fourier-type transforms between finite arrays of ‘sensor’ points. The kernel matrices are unitary and are well-known in group theory; they involve the discrete polynomials of Kravchuk, q-Kravchuk, Meixner and Hahn. In the continuum limit these transforms contract to the fractional Fourier and Hankel integral transforms.

© 2003 Optical Society of America

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