基于五项MSD窗三谱线插值的高精度谐波分析算法

High accuracy analysis of harmonic algorithm based on 5-term maximum-sidelobe-decay window and triple-spectrum-line interpolation

为了解决快速傅里叶变换中存在的频率泄露和栅栏效应的问题,提出一种高精度的五项最大旁瓣(Maximum-sidelobe-decay,MSD)窗插值算法。从时域和频域分别分析了该窗函数和其他常用窗函数,体现出该窗函数的优秀旁瓣特性。用Matlab中的cftool工具拟合出该算法的修正公式,并用该方法对一般信号和频率变动的信号进行仿真分析。对比其他常用的几种窗函数插值算法的结果,表明五项MSD窗三谱线插值算法具有相对更高的精度,幅值相对误差达到10^(-9)%,而且在工频波动的情况下仍具有较高精度。

In order to solve the problems of fence effect and spectral leakage in Fast Fourier Transform analysis, an approach of high accuracy harmonic analysis is proposed, which bases on 5-term Maximum-Sidelobe-Decay window and triple-spectrum-line interpolation. It analyzes the window function and other commonly used window fimction in terms of time and frequency domain, reflecting the excellent characteristics of the sidelobe in the window function. It uses the cftool tool in Matlab to fit the modified formula of the algorithm. Then, it analyzes the general signal and signal of frequency change with the method, comparing with other several commonly used window function and interpolation algorithm results, this method shows a higher accuracy performance. In high accuracy analysis of harmonic algorithm based on 5-term MSD window and interpolation, the relative error of the amplitude has reached 109%, and it also has a good performance when frequency fluctuation happens.