插值FFT估计正弦信号频率的精度分析

对噪声背景中插值FFT方法估计正弦信号频率的精度进行了研究,导出了不加窗和加Hanning窗时频率估计均方根误差与信噪比及FFT长度的关系式;分析了不加窗情况下当信号频率接近FFT频率分辨率Δf的整数倍时,由于插值的方向错误对频率估计精度的影响;指出了不加窗时该方法在噪声背景中的频率估计误差远远大于文2]中用一个特定的纯测试信号得到的结果;讨论了加窗对频率估计误差的影响.最后给出了Monte Carlo模拟实验与理论分析的对比结果.

Accuracy Analysis of Frequency Estimation of Sinusoid Based on Interpolated FFT

The accuracy of the frequency estimation technique of sinusoid based on the interpolated FFT is investigated. Formulas for evaluating the root-mean-square (RMS) error of frequency estimation for different signal-to-noise ratio and different FFT length without weighting window and with Harming window are derived. Study results show that when the frequency of the signal is close to the center of the main lobe of the FTT, due to the inversion of the interpolation direction, the interpolated FFT without weighting window results in large errors in frequency estimation.Therefore in noise background, the frequency estimation error of the interpolated FFT method is much larger than that achieved by Jain in 2] using a given pure test sinusoid signal. The effect of the weighting window on frequency estimation accuracy is also discussed. Computer Monte Carlo simulation results fit well with the fonnulas given in this paper.