The discrete fractional Fourier transform based on the DFT matrix

SERBES A., Durak-Ata L.

SIGNAL PROCESSING, cilt.91, sa.3, ss.571-581, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 91 Sayı: 3
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.sigpro.2010.05.007
  • Dergi Adı: SIGNAL PROCESSING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.571-581
  • Anahtar Kelimeler: Discrete fractional Fourier transform, DFT matrix, Hermite-Gauss functions, Eigentransform matrices, Rotation property, EIGENVECTORS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

We introduce a new discrete fractional Fourier transform (DFrFT) based on only the DFT matrix and its powers. Eigenvectors of the DFT matrix are obtained in a simple-yet-elegant and straightforward manner. We show that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the continuous FrFT. By appropriately combining existing commuting matrices we obtain a new commuting matrix which performs better. We show the validity of the proposed algorithms by computer simulations comparing DFrFT points and continuous FrFT samples for various signals. (C) 2010 Elsevier B.V. All rights reserved.