基于迭代离散时间傅里叶变换插值的高精度频率估计

High-precision Frequency Estimation Based on Iterative DTFT Interpolation

为实现任意波动周期下含噪实正弦信号的高精度频率估计,提出了一种基于迭代离散时间傅里叶变换(discrete-time Fourier transform,DTFT)插值的新型频率估计算法,打破了现有插值算法仅限于固定等间隔离散傅里叶变换(discrete Fourier transform,DFT)谱的局限性。首先,将频谱变换推广应用至任意的广义DTFT谱,通过计算得到适用于任意谱间隔的3谱线方程;进而,根据辅助谱线间隔构建多谱线方程组,通过精确求解得到基于不同插值方式的无偏频率估计解析解;最后,考虑加性噪声影响,采用简单有效的迭代执行方式进一步优化算法性能,确保频率估计的均方误差(mean square error,MSE)在全域内能够一致逼近最优。仿真分析和实验结果表明了算法的有效性和准确性。

To achieve a high-precision frequency estimation of the noisy real sinusoidal signals with any cycles in record,this paper proposes a novel frequency estimation algorithm based on the iterative discrete-time Fourier transform(DTFT)interpolation,breaking the limitation that the existing interpolation algorithm only considers the fixed and equal interval discrete Fourier transform(DFT)spectrum.First,the spectrum transformation is extended to any generalized DTFT spectrum,and a 3-spectral line equation suitable for any spectral interval is obtained by calculation.Then,a multi-spectral line equation set is constructed according to the intervals of the auxiliary spectral lines,and the analytical solution of the unbiased frequency estimation based on different interpolation methods can be obtained.Finally,considering the influence of the additive noise,a simple and effective iterative execution method is used to further optimize the performance of the algorithm to ensure that the mean square error(MSE)of the frequency estimation can be uniformly approximated to the optimum in the entire domain.Simulation analysis and experimental results verify the effectiveness and accuracy of the algorithm.