论文标题
短期免费元转换的不确定性原则
Uncertainty Principles for the Short-time Free Metaplectic Transform
论文作者
论文摘要
由于其在信号处理，携带光学系统，数字算法，光学加密等方面的各种应用，因此近来的自由元容器转换（FMT）近期广受欢迎。但是，FMT不足以对非传播信号进行局部分析，因此，必须引入独特的局部变换，以短时间自由跨度转换（STFMT）。在本文中，我们研究了STFMT。首先，我们提出了STFMT的定义，并提供了FMT域中提出的转换的时间频率分析。其次，我们研究了所提出的转换的基本特性，包括重建公式，moyals公式。 STFMT定义及其性质的出现在一定程度上扩大了高维信号理论的时频表示的发展。最后，我们从量子力学，包括Liebs，Pitts Up，Heisenbergs不确定性原理，Hausdorff-Young，Hardys Up，Beurlings Up，Aboogarithmic Up和Nazarovs UP等量子力学中扩展了一些不同的不确定性原理（UP）。
The free metaplectic transformation (FMT) has gained much popularity in recent times because of its various application in signal processing, paraxial optical systems, digital algorithms, optical encryption and so on. However, the FMT is inadequate for localized analysis of non-transient signals, as such, it is imperative to introduce a unique localized transform coined as the short time free metaplectic transform (STFMT). In this paper, we investigate the STFMT. Firstly, we propose the definition of the STFMT, and provide the time frequency analysis of the proposed transform in the FMT domain. Secondly, we investigate the basic properties of the proposed transform including the reconstruction formula, Moyals formula. The emergence of the STFMT definition and its properties broadens the development of time-frequency representation of higher-dimensional signals theory to a certain extent. Finally, we extend some different uncertainty principles (UP) from quantum mechanics including Liebs, Pitts UP, Heisenbergs uncertainty principle, Hausdorff-Young, Hardys UP, Beurlings UP, Logarithmic UP, and Nazarovs UP which have already been well studied in the FMT domain
