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Fractional Fourier Transform and Its Applications

Fractional Fourier Transform is a type of Linear Conanical Transform, which has an extra free parameter when compared to ordinary Fourier Transform. This free parameter corresponds to the projection of the time-frequency representation of the signal at a certain angle which depends on the parameter value. FrFT has found a wide range of applications in signal and image processing, especially whenever there are time- or space- variant systems or signals are involved. Below, we list our contributions to the area and the applications we have developed based on FrFT.

  • Fractional Fourier Decompositions
  • Image Compression with FrFT
  • Perspective Projections and FrFT

  • References:
    1. I. S. Yetik and A. Nehorai, "Beamforming using the Fractional Fourier Transform," IEEE Transactions on Signal Processing, vol. 51, pp. 1663-1668, June 2003.
    2. I. S. Yetik, M. A. Kutay, H. M. Ozaktas, "Optimization of orders in multi-channel fractional fourier domain filtering circuits and its application to the synthesis of mutual intensity distributions," Applied Optics, vol. 41, pp. 4078-4084, 2002.
    3. I. S. Yetik, M. A. Kutay, H. M. Ozaktas, "Image representation and compression with the fractional Fourier transform," Optics Communications, vol. 197, pp. 275-278, 2001.
    4. I. S. Yetik, H. M. Ozaktas, B. Barshan, L. Onural, "Perspective projections in the space-frequency plane and fractional Fourier transforms," Journal of Optical Society of America A, vol. 12, pp. 2382-2390, Dec. 2000.
    5. I. S. Yetik, H. M. Ozaktas, M. A. Kutay, Fractional Fourier Transform and its Applications,Proceedings of DETC ASME, CD-ROM, 2003.
    6. I. S. Yetik, M. A. Kutay, and H. M. Ozaktas, "Kesirli Fourier donusumu ile imge gosterimi ve sikistirilmasi, in Turkish (Image representation and compression with the fractional Fourier transform)," Sinyal Isleme ve Uygulamalar?, pp. 37-41, 2001.
    7. I. S. Yetik, H. M. Ozaktas, B. Barshan, and L. Onural, "Perspektif donusumu zaman-siklik duzleminde incelenmesi, in Turkish (Perspective projections in the space-frequency plane.) " Sinyal Isleme ve Uygulamalar?, pp. 629-633, 2000.
    8. I. S. Yetik, H. M. Ozaktas, B. Barshan, and L. Onural, "Perspective projections in the space-frequency plane and fractional Fourier transforms," Proceedings of the first IEEE Balkan Conference on Signal Processing, Communications and Circuits, and Systems, 2000.
    9. I. S. Yetik, M. A. Kutay, H. Ozaktas, and H. M. Ozaktas, "Continuous and Discrete Fractional Fourier Domain Decompositions," Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, pp. I:93-96, 2000.