New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit
New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit
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DOI：
10.1155/2009/563265
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发表时间：
2009
影响因子：
1.9
通讯作者：
Xu Guanlei;Wang Xiaotong;Xu Xiaogang
中科院分区：
文献类型：
--
作者：
Xu Guanlei;Wang Xiaotong;Xu Xiaogang
不确定性原理在数学、物理、信号处理等领域有着重要的应用，本文首先从线性正则变换（LCT）的定义出发，利用传统的Pitt不等式，得到了LCT域上一个与LCT参数有关的新的Pitt不等式，然后由这个新的Pitt不等式导出了LCT域上一个新的对数不确定性原理，其与两个LCT的参数相关联。其次，从原函数与LCT的关系出发，导出了LCT域上的一个熵测不准原理和一个Heisenberg测不准原理，它们与LCT参数和有关，并给出了这三个下界只与LCT参数和有关而与和无关的原因。结果表明，有可能的界限趋于零。
The uncertainty principle plays an important role in mathematics, physics, signal processing, and so on. Firstly, based on definition of the linear canonical transform (LCT) and the traditional Pitt's inequality, one novel Pitt's inequality in the LCT domains is obtained, which is connected with the LCT parameters and Then one novel logarithmic uncertainty principle is derived from this novel Pitt's inequality in the LCT domains, which is associated with parameters of the two LCTs. Secondly, from the relation between the original function and LCT, one entropic uncertainty principle and one Heisenberg's uncertainty principle in the LCT domains are derived, which are associated with the LCT parameters and The reason why the three lower bounds are only associated with LCT parameters and and independent of and is presented. The results show it is possible that the bounds tend to zeros.