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Kantor, I.L. and Solodov-nikov, A.S. (1989) Hypercomplex number: An elementary introduction to algebras. Springer-Verlag, New York.

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• 标题: 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

  关键字: 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

  期刊名称: 《Advances in Applied Mathematics》, Vol.3 No.3, 2014-08-27

  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。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.