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The discrete fractional Fourier transform
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Date
2000-05-01
Author
Candan, Çağatay
KUTAY, Mehmet Alper
OZAKTAS, HM
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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.
Subject Keywords
Chirplets
,
Discrete Wigner distributions
,
Hermite–Gaussian functions
,
Time–frequency analysis
URI
https://hdl.handle.net/11511/35494
Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
DOI
https://doi.org/10.1109/78.839980
Collections
Department of Electrical and Electronics Engineering, Article