The Importance of Continuity for Linear Time-Invariant Systems
发布时间：2025-04-30
点击次数：
- 发布时间：
- 2025-04-30
- 论文名称：
- The Importance of Continuity for Linear Time-Invariant Systems
- 发表刊物：
- IEEE Signal Processing Magazine
- 摘要：
- It is widely known that an LTI system $T$ can be completely characterized by its impulse response, and the output signal of $T$ can be computed by the convolution of the input signal with the impulse response of $T$. However, in this note we will show that without the continuity of $T$, these results are not true in general. We construct two discontinuous LTI systems, which have the same impulse response but behave differently. Moreover, the convolution formula does not hold for these systems. We also prove that, for a linear system, the continuity implies the bounded input-bounded output (BIBO) stability, whereas the BIBO stability does not imply the continuity. Therefore, the continuity plays a very important role in LTI systems. However, this concept does not receive much attention as it should have in the literature of signal processing.
- 合写作者：
- Ming Zhang and Xiaoming Chen
- 卷号：
- 37(2)
- 页面范围：
- 77-100
- 是否译文：
- 否
- 发表时间：
- 2020-03-01