离散频谱分析比值校正法幅值和相位的抗噪性分析

摘要

谐波信号离散频谱分析的比值校正法(内插法)在无噪声时是一种准确的校正方法,只存在计算时的舍入误差,但在包含噪声尤其信噪比较低时,校正精度会有所下降,甚至误差很大.研究了比值校正法的幅值与相位加不同的窗函数及加性高斯白噪声时的统计方差公式,并通过不同信噪比下的仿真验证了其准确性.建议避免在归一化频率误差较低的情况下使用加矩形窗的比值校正法来校正相位.%Without noise, Interpolation method for discrete spectrum is an accurate correction method except rounding errors. However, the estimation accuracy can be greatly reduced when a signal corrupted with noise, and even turns out to be meaningless. The paper investigates the influences of windowing and additive White Gaussian Noise on the accuracy of amplitude and phase based on interpolation method. Analytical expressions of the estimator variance for amplitude and phase correction are derived. Simulation results confirm the validity of the presented analysis. We suggest to avoid using interpolation method under the condition that the rectangular window is adopted to correct the phase when the normalization frequency error is small.