傅里叶变换差分求和性质的案例教学法

Case Teaching Method for Difference and Summation Property of Fourier Transform

傅里叶变换性质是“信号与系统”课程中一项非常重要的内容,但学生往往将注意力集中在性质的理论推导和具体表达形式上,忽略了性质背后的物理意义和具体的工程应用。本文以离散时间傅里叶变换的差分/求和性质为例,通过对音乐的幅度谱、雷达动目标显示和图像平滑处理的处理,介绍如何从物理意义和工程实践两个方面加深对傅里叶变换性质的理解。

The Fourier transform properties are very important in the course of Signals and Systems.However,students tend to focus on the theoretical derivation and specific expression of the properties,ignoring the physical meaning behind the properties and specific engineering applications.Taking difference and summation property of discrete-time Fourier transform as an example,the amplitude spectrum of music signal,radar moving target display and image smoothing are introduced to show how to deepen the understanding of the properties of Fourier transform from both physical meaning and engineering practice.