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Frequency estimator of sinusoid based on interpolation of three DFT spectral lines

机译：基于三个DFT谱线内插的正弦频率估计器

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摘要

Highlights•A more general form of DFT interpolation based frequency estimator is proposed.•Spectral lines at arbitrary position in the main or the first side lobe are used.•The formula for calculating the MSE in additive white noise is derived.•Correlation coefficients between the noises with arbitrary intervals are derived.•The RMSE is closer to CRLB than the competing estimators especially at high SNR.AbstractA frequency estimator of sinusoid based on interpolation of three discrete Fourier transform (DFT) spectral lines is proposed. The FFT is performed first on the sampled sinusoid signal and the coarse frequency estimation is made by searching the location of the discrete spectral line with maximum amplitude (the primary spectral line). Fine frequency estimation is made by the interpolation using the primary spectral line and two auxiliary spectral lines located at arbitrary position within the main lobe or the first sidelobe of the frequency spectrum. The formula for calculating the MSE of the proposed estimator in additive white noise is derived. The influence of the interval between the primary spectral line and the auxiliary spectral lines on the MSE is analyzed through theoretical analysis and simulation experiments. To further improve the estimation performance, iterative procedures are used. Simulation results show that the RMSE of the proposed estimator is closer to CRLB than the competing estimators especially at high SNR.
机译： 突出显示 • 提出了一种更通用的基于DFT插值的频率估计器。 • 使用主旁瓣或第一个旁瓣中任意位置的光谱线。 • 得出用于计算加性白噪声中MSE的公式。 • Co得出具有任意间隔的噪声之间的相关系数。 • < ce：para id =“ para0005” view =“ all”>尤其是在高SNR情况下，RMSE比竞争对手的估计值更接近CRLB。 < / ce：simple-para> 摘要 基于三个离散傅立叶变换的插值的正弦频率估计器（提出了DFT）谱线。首先对采样的正弦信号执行FFT，然后通过搜索具有最大幅度的离散频谱线（主频谱线）的位置来进行粗略频率估计。通过使用位于频谱主瓣或第一旁瓣内任意位置的主频谱线和两条辅助频谱线进行插值，可以进行精细的频率估算。推导了在加性白噪声中计算所提出的估计器MSE的公式。通过理论分析和仿真实验，分析了主谱线和辅助谱线之间的间隔对MSE的影响。为了进一步提高估计性能，使用了迭代过程。仿真结果表明，在高信噪比的情况下，所提出的估计器的RMSE比竞争估计器更接近CRLB。

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  • 来源
    《Signal processing》 |2018年第3期|52-60|共9页
  • 作者

    Lei Fan; Guoqing Qi;

  • 作者单位

    College of Information Science and Technology, Dalian Maritime University,School of Information Science and Engineering, Dalian Polytechnic University;

    College of Information Science and Technology, Dalian Maritime University;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Frequency estimation; DFT; Interpolation; Sinusoid;

    机译：频率估计;DFT;插值;正弦波;

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