基于DFT系数极值的单频信号频率的高精度迭代估计方法

High accuracy iterative frequency estimating algorithm based on the extremum of the DFT coefficients

提出了一种基于DFT系数极值的单频信号频率的高精度迭代估计方法,该方法根据DFT谱线使用截弦法解算DFT系数极值所在谱线的位置,进而估计单频信号频率。在估计过程中,直接对DFT幅度最大的谱线进行小数频移以获得新的谱线,从而减少频率采样间隔提高估计精度;同时通过迭代估计消除频率依赖性,提高估计性能。仿真结果表明该方法的频率估计精度在任意频率处均接近于克拉美罗下限,其运算量为Nlog2N+4N次复乘法运算,仅比传统的基于DFT插值的估计算法增加4N次复乘法运算,其中N为DFT运算时所采用的数据点数。

At present, frequency estimation algorithm based on DFT interpolation is widely used because of it＇ s high operation efficiency, but the estimating accuracy is dependent on the signal frequency, and for specific frequency, the estimation performance is bad. To solve this problem, a high accuracy frequency estimation algorithm with lower calculating complexity is proposed. In this algorithm, the signal frequency was estimated by Secant Method based on the DFT samples, and decimal fraction frequency of peak magnitude DFT sample was estimated to generate new DFT samples, thus reducing the DFT sample interval with little calculating burden, then improving the estimating accuracy. In addition, through removing the frequency reliant characteristics of estimation which exist in traditional frequency estimator based on the DFT interpolation, this algorithm increased the iterative estimation. To analyze the performance of the algorithm, a simulation was fulfilled. The simulation results show that the single frequency estimator without iterative estimation has asymptotic estimating variance less than 1.2 times the CRLB, which is better than the traditional frequency estimator based on the DFT interpolation, with calculation labor of N log2N ＋ 2N complex multiplications, and the iterative frequency estimator has estimating variance about CRLB for all signal frequency calculation labor of N log2N ＋ 2N complex multiplications, and N is the number of the DFT samples.