The Superposition Principle of 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 Superposition Principle of Linear Time-Invariant Systems
- 发表刊物：
- IEEE Signal Processing Magazine
- 摘要：
- It is well known that the output signal of a linear time-invariant (LTI) system can be expressed as the convolution of the input signal and the system's impulse response. However, the derivation of this result is not rigorous in the majority of the literature. Because a linear operator defined on an infinite-dimensional space may be discontinuous, the order of the linear operator and the summation cannot be interchanged arbitrarily. Therefore, the superposition principle of LTI systems is only valid for finitely many terms, but not for infinitely many terms. In this note we prove that a necessary and sufficient condition for the superposition principle with infinitely many terms is that the system is linear and continuous.
- 合写作者：
- Ming Zhang and Anxue Zhang
- 卷号：
- 36 (6)
- 页面范围：
- 153-156
- 是否译文：
- 否
- 发表时间：
- 2019-11-15