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S.C. Pei and J. J. Ding, “Eigenfunctions of Fourier and Fractional Fourier Transforms With Complex Offsets and Parameters,” IEEE Trans Circuits and Systems-I: Regular Papers, 2007, Vol. 54, No. 7, pp. 1599-1611.

has been cited by the following article:

• TITLE: Discrete Entropic Uncertainty Relations Associated with FRFT

  AUTHORS: Guanlei Xu, Xiaotong Wang, Lijia Zhou, Limin Shao, Xiaogang Xu

  KEYWORDS: Discrete Fractional Fourier Transform (DFRFT); Uncertainty Principle; Rényi Entropy; Shannon Entropy

  JOURNAL NAME: Journal of Signal and Information Processing, Vol.4 No.3B, October 17, 2013

  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.