The discrete fractional Fourier transform based on the DFT matrix

Authors:
Ahmet Serbes;Lutfiye Durak-Ata
Affiliations:
Yildiz Technical University, Department of Electronics and Communications Engineering, Yildiz, Besiktas, 34349 Istanbul, Turkey;Yildiz Technical University, Department of Electronics and Communications Engineering, Yildiz, Besiktas, 34349 Istanbul, Turkey
Venue:
Signal Processing
Year:
2011

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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.