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The Fractional Fourier Transform and Harmonic Oscillation |
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| Authors: | Kutay M Alper Ozaktas Haldun M |
| Institution: | (1) The Scientific and Technical Research Council of Turkey, The National Research Institute of Electronics and Cryptology (TUBITAK – UEKAE), Atatürk Bulvari no 221, 06100 Kavaklidere, Ankara, Turkey;(2) Department of Electrical Engineering, Bilkent University, 06533 Bilkent, Ankara, Turkey |
| Abstract: | 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. |
| Keywords: | fractional Fourier transform harmonic oscillation Green's function phase space |
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