The Fractional Fourier Transform and Harmonic Oscillation

The ath-order fractional Fourier transform is a generalization ofthe ordinary Fourier transform such that the zeroth-order fractionalFourier transform operation is equal to the identity operation and thefirst-order fractional Fourier transform is equal to the ordinaryFourier transform. This paper discusses the relationship of thefractional Fourier transform to harmonic oscillation; both correspondto rotation in phase space. Various important properties of thetransform are discussed along with examples of commontransforms. Some of the applications of the transform are brieflyreviewed.

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