论文标题
短时四个二次相傅立叶变换及其不确定性原理
Short time quaternion quadratic phase Fourier transform and its uncertainty principles
论文作者
论文摘要
在本文中，我们将复杂的值函数的二次相傅立叶变换扩展到两个变量的四个变量函数的函数。我们称其为四个二次相傅立叶变换（QQPFT）。基于QQPFT和Qutaternion傅立叶变换（QFT）之间的关系，我们获得了QQPFT的Sharp Hausdorff-Young不等式。我们定义了短时四个二次相傅立叶变换（STQQPFT），并探索其某些属性，包括内部产品关系和反转公式。我们发现它与2D四季度歧义函数的关系以及与QQPFT相关的Qugater-wigner-Ville分布，并获得了这三个转换的LIEB的不确定性和熵不确定性原理。
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.
