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

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 (2014) 一类四元数线性正则变换的不确定性原理。 应用数学进展, 3, 134-139. doi: 10.12677/AAM.2014.33020

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