The discrete fractional Fourier transform
Author
Candan, C.
Kutay, M. A.
Haldun M. Özaktaş
Date
2000-05Source Title
IEEE Transactions on Signal Processing
Print ISSN
1053-587X
Publisher
IEEE
Volume
48
Issue
5
Pages
1329 - 1337
Language
English
Type
ArticleItem Usage Stats
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Abstract
We propose and consolidate a definition of the
discrete fractional Fourier transform that generalizes the discrete
Fourier transform (DFT) in the same sense that the continuous
fractional Fourier transform generalizes the continuous ordinary
Fourier transform. This definition is based on a particular set of
eigenvectors of the DFT matrix, which constitutes the discrete
counterpart of the set of Hermite–Gaussian functions. The definition
is exactly unitary, index additive, and reduces to the DFT for
unit order. The fact that this definition satisfies all the desirable
properties expected of the discrete fractional Fourier transform
supports our confidence that it will be accepted as the definitive
definition of this transform.