二维信号四元数加窗偏移线性正则变换的测不准原理
Uncertainty Principles for Quaternion Windowed Offset Linear Canonical Transform of Two Dimensional Signals
摘要：
偏移线性正则变换包含了众多的积分变换，是分析具有更多自由度的非平稳信号的有效工具。本文通过引入一种新的时频变换，即二维四元数信号的四元数加窗偏移线性正则变换，推广了四元数信号的加窗偏移线性正则变换。我们开始我们的调查研究的一些基本性质，建议变换，包括内积关系，能量守恒，再生公式，采用四元数偏移线性正则变换的机械。给出了四元数加窗偏移线性正则变换的Heisenberg-Weyl测不准原理、对数测不准原理和局部测不准原理。最后给出了一个四元数加窗偏移线性正则变换的例子。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
