Linear time-invariant (LTI) systems play a fundamental role in signal processing. Continuity is an important property of LTI systems, without which many conclusions about LTI systems, such as convolution formula and commutative law, are not true in general. However, this concept does not receive as much attention as it should in the literature of signal processing. In this "Lecture Notes" article, we provide a detailed discussion on the importance of continuity for LTI systems. For simplicity, we mainly consider the discrete-time signals and systems.

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线性时不变系统连续性的重要性 [讲义]

线性时不变 (LTI) 系统在信号处理中发挥着重要作用。连续性是 LTI 系统的一个重要性质，没有它，许多关于 LTI 系统的结论，如卷积公式和交换律，一般都是不正确的。然而，这个概念并没有像在信号处理文献中那样受到足够的关注。在这篇“讲义”文章中，我们详细讨论了 LTI 系统连续性的重要性。为简单起见，我们主要考虑离散时间信号和系统。