- 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:
- I. S. Yetik and A. Nehorai, "Beamforming using the Fractional Fourier Transform," IEEE Transactions on Signal Processing, vol. 51,
pp.
1663-1668, June 2003.
- 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.
- 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.
- 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.
- I. S. Yetik, H. M. Ozaktas, M. A. Kutay, Fractional Fourier Transform and its Applications,Proceedings of DETC ASME, CD-ROM, 2003.
- 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.
- 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.
- 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.
- 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.
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