Relations Between Gabor Transforms and Fractional Fourier Transforms and Their Applications for Signal Processing

@article{Pei2006RelationsBG,
  title={Relations Between Gabor Transforms and Fractional Fourier Transforms and Their Applications for Signal Processing},
  author={Soo-Chang Pei and Jian-Jiun Ding},
  journal={IEEE Transactions on Signal Processing},
  year={2006},
  volume={55},
  pages={4839-4850}
}
Many useful relations between the Gabor transform (GT) and the fractional Fourier transform (FRFT) have been derived. First, we find that, like the Wigner distribution function (WDF), the FRFT is also equivalent to the rotation operation of the GT. Then, we show that performing the scaled inverse Fourier transform (IFT) along an oblique line of the GT of f(t) can yield its FRFT. Since the GT is closely related to the FRFT, we can use it for analyzing the characteristics of the FRFT. Compared… CONTINUE READING
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