We investigate the 2D quaternion windowed linear canonical transform (QWLCT) in this paper. Firstly, we propose the new definition of the QWLCT, and then several important properties of newly defined QWLCT, such as bounded, shift, modulation, orthogonality relation, are derived based on the spectral representation of the quaternionic linear canonical transform (QLCT). Secondly, by the Heisenberg uncertainty principle for the QLCT and the orthogonality relation property for the QWLCT, the Heisenberg uncertainty principle for the QWLCT is es- tablished. Finally, we give an example of the QWLCT.

中文翻译：

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二维信号的四元数加窗线性典范变换

在本文中，我们研究了二维四元数窗口线性典范变换（QWLCT）。首先，我们提出了QWLCT的新定义，然后基于四元离子线性典范变换（QLCT）的频谱表示，得出了新定义的QWLCT的一些重要属性，例如有界，移位，调制，正交关系。其次，通过QLCT的Heisenberg不确定性原理和QWLCT的正交关系性质，建立了QWLCT的Heisenberg不确定性原理。最后，我们以QWLCT为例。