Uncertainty inequalities for linear canonical transform
Uncertainty inequalities for linear canonical transform
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DOI：
10.1049/iet-spr.2008.0102
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发表时间：
2009-09
影响因子：
1.7
通讯作者：
Guanlei Xu;Xiaotong Wang;Xiaogang Xu
中科院分区：
文献类型：
--
作者：
Guanlei Xu;Xiaotong Wang;Xiaogang Xu
在p-范数空间（0<p<∞）中，利用Fourier变换与线性正则变换（LCT）之间的关系，导出了与LCT相关的新的Hausdorff-Young不等式.基于导出的Hausdorff-Young不等式，给出了Shannon熵和Renyi熵的不确定性关系.它表明这些关系是变换参数（a，B，c，d）的函数。同时，从Shannon熵的测不准关系出发，导出了LCT域中的Heisenberg测不准关系，该关系对真实的和复信号都成立。此外，给出了加窗分数傅里叶变换的海森堡测不准原理。最后，一个审查的不确定性关系的LCT和其他变换的列表中首次系统。
The novel Hausdorff–Young inequalities associated with the linear canonical transform (LCT) are derived based on the relation between the Fourier transform and the LCT in p-norm space (0<p<∞). Uncertainty relations for Shannon entropy and Renyi entropy based on the derived Hausdorff–Young inequality are yielded. It shows that these relations are functions of the transform parameters (a, b, c, d). Meanwhile, from the uncertainty relation for Shannon entropy the Heisenberg's uncertainty relation in LCT domains is derived, which holds for both real and complex signals. Moreover, the Heisenberg's uncertainty principle for the windowed fractional Fourier transform is obtained. Finally, one review of the uncertainty relations for the LCT and other transforms is listed in tables systematically for the first time.