A new class of superoscillatory functions based on a generalized polar coordinate system
A new class of superoscillatory functions based on a generalized polar coordinate system
复制标题
基于广义极坐标系的一类新型超振荡函数
DOI：
--
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
T. Shushi
中科院分区：
文献类型：
--
作者：
Y. Aharonov;T. Shushi
一个带限信号是否可能具有任意高于其最高傅立叶分量的振荡？常识认为答案是否定的。“与直觉相反的是，事实证明，有一些带限函数的振荡速度可以任意快于它们最快的傅立叶分量。这些是超振荡函数。自发现以来，超振荡在傅里叶分析领域一直很有趣，在量子力学、光学、雷达理论等领域有着广泛的应用。超振荡文献的一个基本目标是找到将用于此类技术的新型超振荡。在本文中，我们介绍了一种基于几何的方法，利用本研究中发展的定向极坐标的概念来构造富类超振荡。我们研究了它们的基本特征，并展示了所提出的方法如何允许产生具有任意数量的超振荡区域和任意数量的变量的超振荡。
Is it possible for a band-limited signal to possess oscillation that is arbitrarily higher than its highest Fourier component? Common knowledge assumed that the answer is ‘No.’ Counterintuitively, it turns out that there are band-limited functions that are able to oscillate arbitrarily faster than their fastest Fourier components. These are the superoscillatory functions. Since their discovery, superoscillations have been intriguing in the world of Fourier analysis, with a vast number of applications in quantum mechanics, optics, and radar theory, among other areas. A basic aim in the literature of superoscillations is to find new types of superoscillations that will be used for such technologies. In this paper, we introduce a geometrical-based method to construct a rich class of superoscillations using the concept of directional polar coordinates, developed in this research. We investigate their basic features and show how the proposed method allows generating superoscillations with an arbitrary number of superoscillatory regions, and with an arbitrary number of variables.