论文标题
线性空间不变的时变问题的波数域中的系统响应分析
System response analysis in wavenumber domain for linear space-invariant time-varying problems
论文作者
论文摘要
作为线性时间不变（LTI）系统的强大工具，系统响应分析也可以应用于所谓的线性空间不变（LSI），但随时间变化的系统，这是传统的LTI问题的双重双重问题。在本文中，我们通过在空间上进行场地分布而不是时间坐标提出了一种针对LSI问题的系统响应分析方法。具体而言，输入和输出信号可以用波数（空间频率）域表示。这样，也可以为LSI系统获得波数域中的系统函数。给定介质的任意输入和时间剖面，可以使用系统函数轻松预测输出。此外，对于复杂的时间系统，所提出的方法允许将其分解为多个更简单的子系统，这些子系统会按时间顺序出现。可以通过将单个子系统的系统功能有效地计算出整个系统的系统功能。
Being a powerful tool for linear time-invariant (LTI) systems, system response analysis can also be applied to the so-called linear space-invariant (LSI) but time-varying systems, which is a dual of the conventional LTI problems. In this paper, we propose a system response analysis method for LSI problems by conducting Fourier transform of the field distribution on the space instead of time coordinate. Specifically, input and output signals can be expressed in the wavenumber (spatial frequency) domain. In this way, the system function in wavenumber domain can also be obtained for LSI systems. Given an arbitrary input and temporal profile of the medium, the output can be easily predicted using the system function. Moreover, for a complex temporal system, the proposed method allows for decomposing it into multiple simpler subsystems that appear in sequence in time. The system function of the whole system can be efficiently calculated by multiplying those of the individual subsystems.
