The discrete fractional Fourier transform

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Candan C., KUTAY M. A., OZAKTAS H.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, cilt.48, sa.5, ss.1329-1337, 2000 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 5
  • Basım Tarihi: 2000
  • Doi Numarası: 10.1109/78.839980
  • Dergi Adı: IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1329-1337
  • Anahtar Kelimeler: chirplets, discrete Wigner distributions, Hermite-Gaussian functions, time-frequency analysis, LINEAR-SYSTEMS, CONVOLUTION, DOMAINS, WIGNER, PRODUCT
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.