Generalized entropic uncertainty principle on fractional Fourier transform

作者: Xu Guanlei , Wang Xiaotong , Xu Xiaogang

DOI: 10.1016/J.SIGPRO.2009.05.014

关键词:

摘要: The entropic uncertainty principle is an element in information theory and plays important role signal processing. Based on the relations between original function definition of fractional Fourier transform (FRFT), two novel principles FRFT domains, which one Shannon entropy other Renyi principle, are derived, associated with parameters. In addition, extended for multiple functions discrete explored as well. These inequalities disclose bounds parameters sampling periods.

参考文章(19)
Xu Guanlei, Wang Xiaotong, Xu Xiaogang, Fractional quaternion Fourier transform, convolution and correlation Signal Processing. ,vol. 88, pp. 2511- 2517 ,(2008) , 10.1016/J.SIGPRO.2008.04.012
X. Guanlei, W. Xiaotong, X. Xiaogang, Uncertainty inequalities for linear canonical transform Iet Signal Processing. ,vol. 3, pp. 392- 402 ,(2009) , 10.1049/IET-SPR.2008.0102
Gerald B. Folland, Alladi Sitaram, The Uncertainty Principle: A Mathematical Survey Journal of Fourier Analysis and Applications. ,vol. 3, pp. 207- 238 ,(1997) , 10.1007/BF02649110
A.I. Zayed, On the relationship between the Fourier and fractional Fourier transforms IEEE Signal Processing Letters. ,vol. 3, pp. 310- 311 ,(1996) , 10.1109/97.544785
G. Cariolaro, T. Erseghe, P. Kraniauskas, N. Laurenti, A unified framework for the fractional Fourier transform IEEE Transactions on Signal Processing. ,vol. 46, pp. 3206- 3219 ,(1998) , 10.1109/78.735297
A. Dembo, T.M. Cover, J.A. Thomas, Information theoretic inequalities IEEE Transactions on Information Theory. ,vol. 37, pp. 1501- 1518 ,(1991) , 10.1109/18.104312
X. Guanlei, W. Xiaotong, X. Xiaogang, Three uncertainty relations for real signals associated with linear canonical transform Iet Signal Processing. ,vol. 3, pp. 85- 92 ,(2009) , 10.1049/IET-SPR:20080019
William Beckner, Inequalities in Fourier analysis Annals of Mathematics. ,vol. 102, pp. 159- ,(1975) , 10.2307/1970980
David Mendlovic, Haldun M. Ozaktas, Fractional Fourier transforms and their optical implementation: I Journal of the Optical Society of America A. ,vol. 10, pp. 1875- 2531 ,(1993) , 10.1364/JOSAA.10.001875