几种基于FFT的频率估计方法精度分析

介绍了噪声背景中正弦信号频率估计的方差下限，对利用FFT主瓣内两条幅度最大谱线进行插值的频率估计方法（Rife-Jane方法和Quinn方法）以及利用FFT相位进行频率插值的方法（分段FFT相位差法和重叠FFT相位差法）的方差进行了理论分析，推导了Quinn方法的频率估计方差计算公式．提出了通过滤波进一步提高分段FFT相位差法的频率估计精度的方法。通过计算机MonteCarlo模拟实验对上述各种方法的频率估计精度以及加窗函数的影响进行了分析并与理论下限进行了比较，指出了每种方法所能达到的估计精度。

Accuracy analysis and comparison of some FFT-based frequency estimators

Frequency estimation techniques based on FFT are widely used. This paper deals with the analysis of variance performances of some FFT based frequency estimators. Firstly, the lower bound of frequency estimation variance of single real sinusoid in additive white Gaussian noise is given. Then the variance performances of two frequency estimators based on the magnitude of FFT coefficients, Rife-Jane method and Quinn method, and two frequency estimators based on the phase of the FFT coefficients, segmented-FFT phase difference method and overlapped-FFT phase difference method, are analyzed. Formula for the evaluation of variance of Qulnn method is derived next. The accuracy of segmented-FFT phase difference method is improved by applying smoothing filter to the two largest spectral lines inside the main lobe of the FFT spectrum. Finally, comparisons of variance performances among different estimators and between each estimator and the Cramer Rao lower bound are made by Monte Carlo simulations for situations without weighting window and with Hanning window, and the accuracy limits for each estimator are also pointed out.