Error analysis of frequency estimation algorithm based on frequency offset correction
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摘要: 介绍了基于频偏校正的频率估计算法原理,给出了算法在高斯白噪声背景下进行复正弦信号频率估计的标准差计算公式.在采样点数为N的情况下,对m的取值进行优化,得到当m取最接近N/3的整数时,算法的标准差达到最小值.Monte Carlo仿真试验结果表明:m取最接近N/3的整数时,频偏校正算法的标准差小于比值法(加汉宁窗)和相位差法,且在偏离FFT(Fast Fourier Transforms)离散谱线的频率变化范围内比较平缓.当信噪比较大时,优化取值后的算法标准差比m取最接近N/2的整数时小,且更加逼近克拉美-劳下限.Abstract: The principle of the frequency estimation algorithm based on frequency offset correction was presented. The computation formula of the frequency estimation-s standard deviation of a complex sinusoidal signal in white Gauss noise was obtained. The value of parameter m was optimized when the data length was N, The algorithm can reach the minimum standard deviation when m was the integer closest to N/3. The Monte Carlo simulation results demonstrate that the algorithm based on frequency offset correction as the integer m is closest to N/3 has lower standard deviation than the interpolation method with Hanning window and the phase difference method, while retaining a flat profile in the frequency range away from the fast Fourier transforms(FFT) discrete spectral line. The m-optimized algorithm-s standard deviation is less and closer to the Cramer-Rao lower bound(CRLB) than the one as m is the integer closest to N/2 when signal noise ratio(SNR) is higher.
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Key words:
- frequency estimation /
- standard deviation /
- error analysis /
- Cramer-Rao lower bound
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