浅析FFT算法中对称关系

Discussion on Symmetry in FFT Algorithm

本文通过分析比较时间抽取FFT算法以及频率抽取FFT算法的基本原理,揭示了FFT算法中存在的对称关系,同时也给出了任意基FFT算法系数矩阵的产生机理。上述的分析比较有助于学生更好地理解和实现FFT算法,同时也可借鉴该算法的思想设计其他算法。

This paper analyzes and compares the basic theory between the decimation-in-time FFT and decimation- in-frequency FFT. The symmetry in FFT algorithm is revealed. Moreover, the generation mechanism of the coefficient matrix in FFT under arbitrary base is given. The symmetry analysis can help student better understand and implement the FFT algorithm. Also, the idea of FFT can be applied when designing .other algorithms.