一类四元数线性正则变换的不确定性原理
Uncertainty Principle for a Kind of Quaternionic Linear Canonical Transform
DOI: 10.12677/AAM.2014.33020,
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作者:
付应雄, 熊 珍：湖北大学数学与统计学学院，武汉
关键词:
四元数；左边四元数线性正则变换；不确定性原理；Quaternion； Left-Sided Quaternionic Linear Canonical Transform； Uncertainty Principle
摘要:
基于左边四元数线性正则变换的相关性态，本文建立左边四元数线性正则变换的不确定性原理。其表明四元数值的信号在时域和频域中方差的乘积具有下界，仅有二维的高斯信号能满足不确定性原理的等式。
Abstract: In this paper, based on the properties of the left-sided quaternionic linear canonical transform (QLCT), an uncertainty principle is established for the left-sided QLCT. It states that the product of the variances of quaternion-valued signals in the spatial and frequency domains has a lower bound and only a 2D Gaussian signal minimizes the uncertainty principle.
文章引用:
付应雄, 熊珍. 一类四元数线性正则变换的不确定性原理[J]. 应用数学进展, 2014, 3(3): 134-139. http://dx.doi.org/10.12677/AAM.2014.33020
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