基于主瓣宽度多谱线插值的高精度快速谐波分析算法

A Precise and Rapid Algorithm for Harmonic Analysis Based on Multi-Spectrum-Line in Main Lobe Width Interpolation FFT

根据窗函数的主瓣宽度提出了一种多谱线插值算法,结合采样率最终确定参与插值的谱线根数。根据窗函数的主瓣内任意相邻两根谱线之间的相位差为π这一规律,提出了一种快速算法,说明无论采用多少根谱线参与运算,计算某次谐波参数仅需要1次求模运算,大大降低了计算复杂度,节约了计算时间。利用不同阶次的Hanning自乘法窗仿真实验表明,多谱线插值算法在拟合阶次较低的情况下,该算法的精度比常用双谱线和三谱线更高,且大大节约了计算量。

This paper has induced multi-spectrum-line interpolation algorithm based on main-lobe width.At the same time,we have proved that the phase difference of any two adjacent spectrum lines isπ.According to this rule,this paper has induced a rapid algorithm so that square root is only calculated one time when we analyze some harmonic parameters.Based on the different order’s hanning selfmultiplication windows,the simulation results have shown that the multi-spectrum-line interpolation algorithm has higher precision than double/triple-spectrum-line interpolation algorithm especially when the order of polynomial is lower than two others if obtaining same precision and the rapid algorithm can save calculation amount greatly.