TITLE:
Generalized Discrete Entropic Uncertainty Relations on Linear Canonical Transform
AUTHORS:
Yunhai Zhong, Xiaotong Wang, Guanlei Xu, Chengyong Shao, Yue Ma
KEYWORDS:
Discrete Linear Canonical Transform (DLCT); Uncertainty Principle; Rényi Entropy; Shannon Entropy
JOURNAL NAME:
Journal of Signal and Information Processing,
Vol.4 No.4,
November
12,
2013
ABSTRACT: Uncertainty
principle plays an important role in physics, mathematics, signal processing
and et al. In this paper, based on
the definition and properties of discrete linear canonical transform (DLCT), we
introduced the discrete HausdorffYoung inequality. Furthermore, the generalized
discrete Shannon entropic uncertainty relation and discrete Rényi entropic
uncertainty relation were explored. In addition, the condition of equality via Lagrange
optimization was developed, which 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 touch their lowest bounds. On
one hand, these new uncertainty relations enrich the ensemble of uncertainty
principles, and on the other hand, these derived bounds yield new understanding
of discrete signals in new transform domain.