快速傅里叶变换(FFT)教学改革的探索与实践

An Exploration and Practice of Teaching Reform in Fast Fourier Transform (FFT)

摘要: 快速傅里叶变换因其高效的计算特性成为数字信号处理的核心工具，但其数学推导与时–频转换机理的高度抽象常给课堂教学带来障碍。为解决这一难点，本文在系统梳理傅里叶级数及连续、离散傅里叶变换理论体系的基础上，以实测风速波动信号为例，设计并实现逐阶频率叠加的可视化教学方案，有助于学习者直观把握各频率分量的物理意义与信号重建机理。

Abstract: The Fast Fourier Transform (FFT), due to its computational efficiency, has become a fundamental tool in digital signal processing. However, its abstract mathematical derivation and the underlying principles of time-frequency conversion often pose challenges in classroom instruction. To address this issue, this study systematically reviews the theoretical framework of Fourier series as well as continuous and discrete Fourier transforms. Using measured wind speed fluctuation signals as a case study, a step-by-step frequency superposition visualization scheme is designed and implemented. This approach facilitates learners’ intuitive understanding of the physical meaning of individual frequency components and the mechanism of signal reconstruction.