《信号与系统》课程中叠加性与均匀性的探讨
Exploring Superposition and Homogeneity in “Signal and System” Course

叠加性和均匀性是《信号与系统》课程中的核心概念，是理解线性特性和判断线性系统的基础。然而，现有教材中普遍缺乏具备叠加性但不具备均匀性，以及具备均匀性但不具备叠加性的具体实例。教学实验结果显示，学生对这两个概念的理解普遍存在不足。对叠加性和均匀性的关系进行了研究，证明了实数域内叠加性蕴含均匀性的结论，并构造了两类非线性系统实例。研究结果丰富了现有教材内容，提示教学过程中有必要加强探究性与启发式的讨论。
Superposition and homogeneity are core concepts in the “Signals and Systems” course, forming the foundation for understanding linear properties and identifying linear systems. However, current textbooks generally lack specific examples that demonstrate systems possessing superposition but not homogeneity, or vice versa. Teaching experiments reveal a widespread deficiency in students’ comprehension of these two concepts. This study explores the relationship between superposition and homogeneity, proving that superposition implies homogeneity in the real domain, and presents two types of nonlinear system examples. The findings supplement existing textbook content and highlight the need for inquiry-based, heuristic discussions in the teaching process.