基于多项式逼近的单峰谱线插值算法在间谐波分析中的应用

快速傅里叶变换在非同步采样和非整数周期截断的情况下存在较大误差，无法获得较精确的间谐波参数值。现有单峰谱线插值算法可以提高间谐波频率、相位和幅值的计算精度，但修正公式计算复杂，影响检测精度。为此，文章提出了一种基于多项式逼近的单峰谱线插值算法，利用距间谐波频点最近的单根离散频谱幅值估计出待求间谐波的幅值，并利用多项式逼近方法推导出幅值、频率及相位的修正公式，基于该方法，推导了一些常用窗函数的修正公式。通过与现有单峰和双峰谱线插值算法在噪声情况下的仿真比较，证明了该方法易于实现，能有效减小估计偏差，提高数据检测精度。

Application of Polynomial Approximation Based Single Peak Spectral Lines Interpolation Algorithm in Interharmonic Analysis

The fast Fourier transform (FFT) will bring on higher error under nonsynchronous sampling and truncated non-integral period, thus more accurate interharmonic parameter values cannot be obtained. Existing single peak spectral lines interpolation algorithm can improve computation accuracy of frequency, phase and amplitude of interharmonic, however the computation of modified formula is complex, so the detection precision will be affected. For this reason, the authors propose a polynomial approximation based single peak spectral lines interpolation algorithm, the amplitude of interharmonic is to be solved by the amplitude of single discrete spectrum that is most close to interharominic frequency point, and by use of polynomial approximation the modified formulae for amplitude, frequency and phase are derived. Based on this method, the modified formulae for common used window functions are derived. By means of comparing simulation results with exiting single and double peak spectral lines interpolation algorithms under noise environment, it is proved that the proposed method is easy to implement; the estimation deviation can be effectively reduced; and the data detection accuracy can be improved.