基于FFT的快速高精度正弦信号频率估计算法

A Fast and Accurate Algorithm for Frequency Estimation of Sinusoid Signal Based on FFT

提出了一种新的基于FFT的快速高精度正弦信号频率估计算法。通过分析Jacobsen算法和傅里叶系数插值迭代算法的性能,指出Jacobsen算法计算简单,精度不高;傅里叶系数插值迭代算法精度较高,但需要进行两次迭代,每次迭代均需计算两点的FFT系数,计算量较大。结合这两种算法,文中提出一种改进的高精度算法。该算法采用Jacobsen算法作为迭代初值,仅需进行一次迭代就能达到原迭代算法两次迭代的性能。仿真结果表明该算法在FFT信噪比门限以上全频段估计的均方根误差十分接近克拉美罗下限,具有较强的抗噪性能,且计算量较少,易于实时实现。

A fast and accurate algorithm based on FFT for frequency estimation of sinusoid signal is proposed in this paper. The performances of Jacobsen algorithm and Fourier-coefficient-interpolation iterative algorithm are investigated in this paper. It shows that Jacobsen algorithm has a less computational load, but poor precision, and the Fourier-coefficient-interpolation iterative algo- rithm has higher precision, but it needs two iterations. Because for each iteration, FFT coefficients of two frequency points are need to computed, it will result in a great computation burden. By combining the two algorithms, an improved approach is pro- posed. The improved approach iterates once with the initial value from Jacobsen algorithm and the performance is nearly the same as two iterations of original iterative algorithm. Simulation results indicate that the frequency estimation variance of this approach approaches to CRLB （Cramer-Rao Lower Bound） throughout the frequency band and performs high anti-noise property. The ap- proach is convenient for real-time realization in real applications due to the less calculation load.