如何讲好时域取样定理

How to Explain the Sampling Theorem in Time Logically

时域取样定理是"信号与系统"和"数字信号处理"等课程的重要内容,但是,目前高等院校普遍使用的国内外经典教材对这部分内容论述不够清晰,没有证明连续时间信号与离散时间信号频谱的关系,尤其是引入了理想冲激取样过程,物理意义不明确,影响了学生理解。本文对时域取样定理进行了深入的思考,提出了两种讲解思路,教学实践表明,对增强学生对该内容的理解,提高授课质量,有较强的针对性。

The sampling theorem in time is very important in the courses of Signals and Systems and Digital Signal Processing. But it has not been explained logically in the books which have been used widely in colleges and universities,and the relationship between the spectrum in frequency domain of continuous-time signal and that of discrete-time signal has not been proved, especially the physical meanings of impulse-train sampling are illogical.So some students have difficult in comprehending the sampling theorem.Two methods have been used in teaching practices which are proposed in this paper, the efficiency testifies that the methods are beneficial to improve teaching effect.