本文我在北航读研时主修《现代偏微分方程》时花费一个多月时间写的期末报告，里面系统阐述了快速傅里叶变换的算法原理及其在数字信号处理等工程技术中的应用。介绍了一维DFT的基2 FFT 算法频域抽取和时域抽取FFT的短发原理和编程步骤。最后在附录中给出了一维DFT的基2 FFT 算法（包括频域抽取的FFT和IFFT算法、时域抽取的FFT和IFFT算法），一维任意非基2 FFT算法，二维DFT的基2 FFT 算法以及二维DFT的任意非基2 FFT 算法的详细的Visual C++程序。-The paper systematically expounded the fast Fourier transform algorithm and its application in digital signal processing applications such as engineering technology . Introduced a one-dimensional DFT of the base 2 FFT algorithm for extraction and time domain frequency domain FFT of the short hair extraction principles and programming steps. Finally, the appendix gives the one-dimensional DFT of the base 2 FFT algorithm (including the extraction of the FFT frequency domain and IFFT algorithms, time domain FFT and IFFT algorithms extracted), one-dimensional arbitrary non-base 2 FFT algorithm, the basic two-dimensional DFT 2 FFT algorithm and two-dimensional DFT of any non-base 2 FFT algorithm in detail Visual C++ program.