正弦波频率估计的修正Rife算法

分析了Rife算法的性能，指出当信号频率位于离散傅里叶变换（Discrete Fourier Transform，DFT）两个相邻量化频率点的中心区域时，Rife算法精度很高，其均方根误差接近克拉美-罗限（Cramer-Rao Lower Bound，CRLB），但当信号频率位于量化频率点附近时，Rife算法精度降低。本文提出了一种修正Rife（M-Rife）算法，通过对信号进行频移，使新信号的频率位于两个相邻量化频率点的中心区域，然后再利用Rife算法进行频率估计。仿真结果表明本算法性能不随被估计信号的频率分布而产生波动，整体性能优于牛顿迭代法（一次迭代）。接近二次迭代，在低信噪比条件下不存在发散问题，性能比牛顿迭代稳定。本算法易于硬件实现。

Modified Rife Algorithm for Frequency Estimation of Sinusoid Wave

The performance of the Rife algorithm is analyzed.When the signal frequency locates in the area near the midpoint of two neighboring discrete frequencies, RMSE(root mean square error) of the frequency estimation is close to CRLB(Cramer-Rao lower bound),but the performance is poor when the signal frequency is near the discrete frequency.A modified Rife(M-Rife) algorithm is presented by moving the signal frequency to the midpoint of two neighboring discrete frequencies and then the frequency is estimated by Rife algorithm.Simulation results show that the performance of M-Rife is better than that of Rife algorithm,RMSE is less than that of one iteration of Newton method,and close to that of two iterations.Under the condition of low SNR,M-Rife has not divergence problem and is more stable than Newton method.Furthermore,the algorithm is easy to be implemented by the hardware.