The discrete fractional Fourier transform based on the DFT matrix

SERBES A., Durak-Ata L.

SIGNAL PROCESSING, vol.91, no.3, pp.571-581, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 91 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.1016/j.sigpro.2010.05.007
  • Journal Name: SIGNAL PROCESSING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.571-581
  • Keywords: Discrete fractional Fourier transform, DFT matrix, Hermite-Gauss functions, Eigentransform matrices, Rotation property, EIGENVECTORS
  • Yıldız Technical University Affiliated: Yes

Abstract

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.