短时四元数二次相位傅里叶变换及其测不准原理
Short time quaternion quadratic phase Fourier transform and its uncertainty principles
摘要：
本文将复值函数的二次相位傅里叶变换推广到二元四元数函数的二次相位傅里叶变换。我们称之为四元数二次相位傅里叶变换（QQPFT）。基于四元数傅里叶变换（QFT）与量子量子点变换的关系，得到了量子点变换的Hausdorff-Young不等式.定义了短时四元数二次相位傅里叶变换（STQQPFT），并研究了它的一些性质，包括内积关系和反演公式。我们发现它与二维四元数模糊函数和与QQPFT相关的四元数Wigner-Ville分布的关系，并得到这三种变换的Lieb不确定性和熵不确定性原理。
英文摘要：
In this paper, we extend the quadratic phase Fourier transform of a complex valued functions to that of the quaternion valued functions of two variables. We call it the quaternion quadratic phase Fourier transform (QQPFT). Based on the relation between the QQPFT and the quaternion Fourier transform (QFT) we obtain the sharp Hausdorff-Young inequality for QQPFT. We define the short time quaternion quadratic phase Fourier transform (STQQPFT) and explore some of its properties including inner product relation and inversion formula. We find its relation with that of the 2D quaternion ambiguity function and the quaternion Wigner-Ville distribution associated with QQPFT and obtain the Lieb's uncertainty and entropy uncertainty principles for these three transforms.
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