The quaternion ambiguity function is an expansion of the standard ambiguity function using quaternion algebra. Various properties such as linearity, translation, modulation, Moyal’s formula and inversion identity are studied in detail. In addition, an interesting interaction between the quaternion ambiguity function and the quaternion Fourier transform is demonstrated. Based on these facts, we seek for several versions of the uncertainty inequalities associated with the proposed quaternion ambiguity function.

中文翻译：

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与四元数模糊函数相关的不等式

四元数模糊度函数是使用四元数代数对标准模糊度函数的扩展。详细研究了各种性质，如线性、平移、调制、莫亚尔公式和反演恒等式。此外，还演示了四元数模糊度函数和四元数傅里叶变换之间有趣的相互作用。基于这些事实，我们寻求与所提出的四元数模糊函数相关的不确定性不等式的几个版本。