基于全相位FFT双谱线插值的频率估计算法

    A Frequency Estimation Algorithm Based on All-phase FFT Bispectral Line Interpolation

    • 摘要: 快速有效地估计正弦信号的频率在雷达信号处理、通信、电网谐波检测和电子对抗等领域有着重要的作用。现有的全相位内插迭代频率估计通常直接采用全相位快速傅里叶变换(apFFT)谱中心线左右两侧半个频率分辨率的谱线插值,当插值谱线的频率离真实频率相差较大时,其谱线的幅值较小,导致其在低信噪比时估计误差较大。为此,文中提出了一种改进的全相位内插法,该方法利用apFFT频谱做双谱线插值,采用两根幅值最高的谱线做幅值比,推导出频偏和幅值比的关系,进而获得频率估值。仿真结果表明,相比于全相位内插迭代算法,所提方法在不同频偏下的估计均方根误差表现出了更好的平稳性及更小的误差,并且在高信噪比时,频率估计性能逼近克拉美-罗下界。

       

      Abstract: Fast and effectively estimating the frequency of sinusoidal signals plays an important role in fields such as radar signal processing, communication, power grid harmonic detection and electronic countermeasures. The existing all-phase interpolation iterative frequency estimation usually uses the spectral line interpolation of half frequency resolution on both sides of the all-phase FFT (apFFT) spectral center line directly. When the frequency of the interpolated spectral line is much different from the true frequency, the amplitude of the spectral line is small, resulting in a large estimation error at low signal-to-noise ratio. In this paper, an improved all-phase interpolation method is proposed, which uses the apFFT spectrum for bispectral line interpolation, and uses the two spectral lines with the highest amplitude as the amplitude ratio to derive the relationship between frequency offset and amplitude ratio, thereby obtains the frequency estimation. Simulation results show that compared with the all-phase interpolation iterative algorithm, the proposed method has better stationarity and smaller error in estimation root mean square error under different frequency biases, and the frequency estimation performance approaches the Cramer-Rao lower bound at high signal-to-noise ratio.

       

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