Discrete Entropic Uncertainty Relations Associated with FRFT

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DOI: 10.4236/jsip.2013.43B021    3,260 Downloads   4,139 Views   Citations

ABSTRACT

Based on the definition and properties of discrete fractional Fourier transform (DFRFT), we introduced the discrete Hausdorff-Young inequality. Furthermore, the discrete Shannon entropic uncertainty relation and discrete Rényi entropic uncertainty relation were explored. Also, the condition of equality via Lagrange optimization was developed, as shows that if the two conjugate variables have constant amplitudes that are the inverse of the square root of numbers of non-zero elements, then the uncertainty relations reach their lowest bounds. In addition, the resolution analysis via the uncertainty is discussed as well.

Cite this paper

G. Xu, X. Wang, L. Zhou, L. Shao and X. Xu, "Discrete Entropic Uncertainty Relations Associated with FRFT," Journal of Signal and Information Processing, Vol. 4 No. 3B, 2013, pp. 120-124. doi: 10.4236/jsip.2013.43B021.

Conflicts of Interest

The authors declare no conflicts of interest.

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