Time-frequency duality
Time-frequency duality
复制标题
时频二象性
DOI：
--
复制
发表时间：
1964
影响因子：
2.5
通讯作者：
P. Bello
中科院分区：
文献类型：
--
作者：
P. Bello
本文提出了一种称为时频对偶的概念，它适用于一类称为通信-信号处理网络的网络。这种网络包括基本元件的互连，如滤波器、混频器、延迟线等。时频二元性的有用性源于这样一个事实，即除了时间和频率所扮演的角色互换之外，物理上可能完全不同的两种情况可以具有相同的行为模式。因此，检测或估计问题的解可以直接从对偶问题的解中找到，如果已知的话，只需将变量和量替换为它们的对偶即可。本文通过在频谱分析之前通过最佳选通操作测量散射介质的传递函数的问题来说明时频对偶的应用。从时频二元性中获得的另一个好处是产生了通信信号处理技术的新思想。我们通过构建Kineplex通信系统的对偶来说明这种类型的好处。第三个好处是能够用另一种方式看待沟通问题，从而获得对沟通问题的额外洞察力。时变线性信道的特性说明了这一优点。通过定义对偶系统函数，证明了这种信道可以在时间和频率变量上以一种有趣的对称方式来表征。
This paper develops a concept of duality, called time-frequency duality, which is applicable to a class of networks called communication-signal-processing networks. Such networks consist of an interconnection of basic elements such as filters, mixers, delay lines, etc. The usefulness of time-frequency duality stems from the fact that two situations which may be quite distinct physically can have identical behavior patterns except for an interchange of the roles played by time and frequency. As a result, the solution to a detection or estimation problem may be found directly from the solution of the dual problem, if known, merely by replacing variables and quantities by their duals. This application of time-frequency duality is illustrated in the paper by the problem of measuring the transfer function of a scatter medium by means of an optimal gating operation prior to spectrum analysis. Another benefit to be obtained from time-frequency duality is the generation of new ideas for communication signal processing techniques. We illustrate this type of benefit by constructing the dual of the Kineplex communication system. A third benefit is the additional insight gained into a communication problem by the ability to look at it in another way. This benefit is illustrated by the characterization of time-variant linear channels. It is demonstrated that such channels may be characterized in an interesting symmetrical manner in time and frequency variables by defining dual system functions.