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 di...

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Bibliographic Details
Published in:Nonlinear dynamics 2002-07, Vol.29 (1-4), p.157-172
Main Authors: M Alper Kutay, Ozaktas, Haldun M
Format: Article
Language:English
Subjects:
Fourier transforms
Harmonic oscillation
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Summary: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.
ISSN:0924-090X
1573-269X
DOI:10.1023/A:1016543123400