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      The discrete fractional Fourier transform

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      Author
      Candan, C.
      Kutay, M. A.
      Haldun M. Özaktaş
      Date
      2000-05
      Source Title
      IEEE Transactions on Signal Processing
      Print ISSN
      1053-587X
      Publisher
      IEEE
      Volume
      48
      Issue
      5
      Pages
      1329 - 1337
      Language
      English
      Type
      Article
      Item Usage Stats
      253
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      409
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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.
      Keywords
      Chirplets
      Discrete Wigner Distributions
      Hermite–gaussian functions
      Time–frequency Analysis
      Permalink
      http://hdl.handle.net/11693/11130
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/78.839980
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      • Department of Electrical and Electronics Engineering 3524
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