论文标题
四维信号的四个维度信号的四个窗口窗口的不确定性原理偏移偏移量
Uncertainty Principles for Quaternion Windowed Offset Linear Canonical Transform of Two Dimensional Signals
论文作者
论文摘要
包含众多积分变换的偏移线性规范变换是一种有前途的工具，用于分析具有更高自由度的非平稳信号。在本文中，我们通过引入一种新型的时频转换，即2D Quaternion价值信号的Quaternion窗口偏移线性变换，将窗户偏移线性转换概括为四基因值信号。我们通过研究所提出的转换的一些基本特性来启动我们的研究，包括内部产品关系，节能和复制公式，通过采用季节偏移偏移线性转换的机制。对于第四座窗口偏移线性典范变换，也得出了一些不确定性原则，例如海森堡 - 韦尔，对数和局部不确定性原理。最后，我们给出了一个四个窗户偏移线性典型变换的示例。
The offset linear canonical transform encompassing the numerous integral transforms, is a promising tool for analyzing non-stationary signals with more degrees of freedom. In this paper, we generalize the windowed offset linear canonical transform for quaternion-valued signals, by introducing a novel time-frequency transform namely the quaternion windowed offset linear canonical transform of 2D quaternion-valued signals. We initiate our investigation by studying some fundamental properties of the proposed transform including inner product relation, energy conservation, and reproducing formula by employing the machinery of quaternion offset linear canonical transforms. Some uncertainty principles such as Heisenberg-Weyl, logarithmic and local uncertainty principle are also derived for quaternion windowed offset linear canonical transform. Finally, we gave an example of quaternion windowed offset linear canonical transform.
