基于四谱线插值FFT的谐波分析快速算法

A rapid algorithm for harmonic analysis based on four-spectrum-line interpolation FFT

由于非同步采样和非整周期截断导致快速傅里叶变换(FFT)不能准确地分析出谐波参数,加窗和插值算法经常被用来改善FFT的计算精度。在信号加窗条件下,基于四谱线插值的FFT算法基础上进行快速算法研究。该算法通过分析加窗后信号的频域表达式,利用真实谐波点附近的4根最大谱线值确定实际谱线的位置,对该次谐波进行频率、幅值和相位等参数估计。并且通过多项式拟合的方式推导出了4种典型窗函数的修正公式。根据窗函数主瓣内任意相邻谱线相位相差π的规律,提出一种快速算法,计算某次谐波开方计算量仅需要1次,大大节约了计算复杂度和计算时间。仿真实验表明,四谱线插值算法在拟合阶次较低的情况下,不仅可以获得比常用双谱线和三谱线更高的精度,还具有对偶次谐波检测精度远胜于双、三谱线插值算法的优点。

In the case of non-synchronous sampling and in non-integral period tnmcation, the fast Fourier transform （FFT） can＇t analyze harmonic parameters correctly. So the window functions and interpolation algorithms are made to improve the accuracy of harmonic parameter computation by FFT. This paper derives an algorithm based on four-spectrum-line interpolation. This algorithm uses the four most spectrum lines around true location to computer the accuracy position of the harmonic spectrum line through analyzing the discrete-time Fourier transform of the windowed signal. Then the true values of frequency, amplitude and phase can be calculated. Based on four-spectrum-line interpolation algorithm, this paper gives four practical rectification formulas by using the polynomial approximation method. It is proved that the phase difference of any two adjacent spectrum is n. According to this rule, this paper induces a rapid algorithm so that square root is only calculated one time when analyzing some harmonic parameters. The algorithm can save computing complexity and computing time greatly. The simulation results show that the four-spectrum-line interpolation algorithm has higher precision than double/triple- spectrum-line interpolation algorithm especially when estimating the even harmonics and the order of polynomial is lower than two others if obtaining same precision.