基于窗函数补零拟合的插值补零FFT谐波分析算法

Interpolated zero-padded FFT algorithm for harmonic analysis based on zero-padded window function fitting

工程上谐波分析通常采用计算量相对较小的快速傅里叶变换(FFT),同时为减少栅栏效应和频谱泄露通常采用插值算法。FFT对数据窗长度有特定要求,例如2/3/4等整数次幂。针对数据窗长度为非整数次幂情况,提出一种改进插值补零FFT谐波测量算法,算法核心在于将补零FFT插值校正转变为基于补零窗函数的频谱响应的拟合校正。以基2为例,对非2整数次幂数据窗加5项最快旁瓣衰减速率窗修正,再补零使得数据窗长度满足2的整数次幂,最后进行改进插值FFT计算。所提算法适用于任意窗函数补零且无须推导修正公式。仿真与实验结果验证该算法在谐波分析方面的有效性。

Fast fourier transform(FFT)is commonly used in engineering for harmonic analysis due to relatively low computational complexity,and interpolation algorithm is usually used to reduce fence effect and spectrum leakage.However,FFT make sure that the length of the data window must satisfy certain conditions,such as 2/3/4 or other inter powers.Aiming at the fact that the length of the data window is a non-integer power,an improved interpolation zero-padded FFT harmonic measurement algorithm is proposed.The core of the algorithm is to transform the interpolation correction of the zero-padded FFT into the fitting correction of the spectral response based on the zero-padded window function.Considering 2-radix,when the length of the data window is non-2 integer power,this paper uses 5-term maximum side lobe decay speed window to correct the data,and then makes the length of the data window satisfy 2 integer power by zero padding,finally calculates FFT with improved interpolated algorithm.The proposed algorithm is suitable for any zero-padded window function and avoids to derive a modified formula.Simulation and experimental results verify the effectiveness of the algorithm in harmonic analysis.