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On Fractional Fourier Transform Moments Based On Ambiguity Function
Sedigheh Ghofrani
Pages - 1 - 11     |    Revised - 31-03-2011     |    Published - 04-04-2011
Volume - 5   Issue - 1    |    Publication Date - March / April 2011  Table of Contents
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KEYWORDS
Fractional Fourier Transform, Fractional Moments, Ambiguity Function, Filtering
ABSTRACT
The fractional Fourier transform can be considered as a rotated standard Fourier transform in general and its benefit in signal processing is growing to be known more. Noise removing is one application that fractional Fourier transform can do well if the signal dilation is perfectly known. In this paper, we have computed the first and second order of moments of fractional Fourier transform according to the ambiguity function exactly. In addition we have derived some relations between time and spectral moments with those obtained in fractional domain. We will prove that the first moment in fractional Fourier transform can also be considered as a rotated the time and frequency gravity in general. For more satisfaction, we choose five different types signals and obtain analytically their fractional Fourier transform and the first and second-order moments in time and frequency and fractional domains as well.
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1 V. Namis, “The fractional order Fourier transform and its application to quantum mechanics,” Journal of Inst. Maths Applics. , 25, pp. 241- 265, 1980.
2 A. C. McBride, and F. H. Kerr, “On Namias’s fractional Fourier transform,” IMA Journal of applied mathematics, 39, pp. 159-m175, 1987.
3 L. B. Almedia, “The fractional Fourier transform and time- frequency representations,” IEEE Trans. On Signal Processing, Vol. 42, No. 11, pp. 3084- 3091, Nov. 1994.
4 H. M. Ozaktas, N. Erkaya, and M. A. Kutay, “Effect of fractional Fourier transformation on time- frequency distributions belonging to the Cohen class,” IEEE Signal Processing Letters, Vol. 3, No. 2. Feb. 1996.
5 R. Saxena, and K. Singh, “Fractional Fourier transform: a novel tool for signal processing,” Journal of Indian Inst. Science, 85, pp. 11- 26, 2005.
6 T. Alieva, and A. Barbe, “Fractional Fourier and radon-wigner transforms of periodic signals,” Elsevier Signal Processing Journal, vol. 69, pp. 183- 189, 1998.
7 M. A. Kutay, H. M. Ozaktas, O. Arikan, and L. Onural, “Optimal filtering in fractional Fourier domains,” IEEE Trans. On Signal Processing, Vol. 45, No. 5, pp. 1129- 1143, May. 1997.
8 M. F. Erden, M. A. Kuaty, and H. M. Ozaktas, “Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration,” IEEE Trans. On Signal Processing, Vol. 47, No. 5, pp. 1458- 1462, May 1999.
9 S. N. Sharma, R. Saxena, and S. C. Saxena, “Tuning of FIR filter transition bandwidth using fractional Fourier transform,” Elsevier Signal Processing Journal, vol. 87, pp. 3147- 3154, 2007.
10 L. Durak, and S. Aldirmaz, “Adaptive fractional Fourier domain filtering,” Elsevier Signal Processing Journal, Article in Press.
11 T. Alieva, and M. J. Bastiaans, “On fractional Fourier transform moments,” IEEE Signal Processing Letters, vol. 7, no. 11, pp. 320- 323, November 2000.
12 L. Stankovic, T. Alieva, M. J. Bastiaans, “Time- frequency analysis based on the windowed fractional Fourier transform,” Elsevier Signal Processing Journal, vol. 83, pp. 2459- 2468, 2003.
13 L. Cohen, “Time-frequency distributions - a review,” Proceedings of the IEEE, vol. 77, no. 7, pp. 941-980, July 1989.
14 L. Chen, D. Zhao, “Application of fractional Fourier transform on spatial filtering,” Elsevier Optik Journal, vol. 117, pp. 107- 110, 2006.
15 S. Shinde, and V. M. Gadre, “An uncertainty principle for real signals in the fractional Fourier transform domain,” IEEE Trans. On Signal Processing, Vol. 49, No. 11, pp. 2545- 2548, Nov. 2001.
Dr. Sedigheh Ghofrani
Azad University - Iran
s_ghofrani@azad.ac.ir