相减策略的含噪多频实信号频率估计算法

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摘要为抑制频谱泄漏对多频实信号频率估计的影响，提出一种新的频率估计算法。首先，利用FFT法和相减策略对采样信号进行处理，逐步得到各分量的频谱最大值索引，以及各分量频谱偏移量和复幅值粗略值；其次，构造包含所有非待估计频率分量的参考信号，利用相减策略从采样信号中减去参考信号，得到待估计的单频复信号，并对其频谱进行两点插值计算，得到该分量较精确的频谱偏移量和复幅值；然后，通过相减策略和频谱分析，逐步得到所有分量较精确的频谱偏移量和复幅值；最后，通过迭代计算得到各分量精确的频率估计值。同时，可得到各分量精确的幅值和初相位。在无噪声、不同频率间隔等条件下进行了频率仿真实验。结果表明：所提算法有效抑制了频谱泄漏的影响，提高了多频实信号的频率估计精度，频率估计值的均方误差比其他优秀算法更靠近克拉美罗下限。
关键词：频率估计；相减策略；频谱泄漏；多频实信号

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	陈鹏1
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	刘春华2
	沈廷鳌3
	乐开白2

关键词 ：频率估计, 相减策略, 频谱泄漏, 多频实信号

Abstract：to suppress the spectrum leakage influence on frequency estimation for multi-tone real values sinusoid signal, a novel frequency estimation algorithm is proposed. Firstly, the FFT algorithm and a subtraction strategy are used to preprocess the sampled signal, and the spectrum index of maximum spectrum of each frequency component is obtained gradually, and coarse values of spectrum offset and complex amplitude of all frequency components are calculated subsequently. Secondly, the reference signal containing all non-estimated frequency components is constructed, and the reference signal is subtracted from the sampled signal by a subtraction strategy to obtain the estimated single-tone complex value signal, and it’s more accurate estimation values of spectrum offset and complex amplitude are calculated by two points interpolation for the spectrum of estimated signal. Then, the more accurate estimation values of frequency offset and complex amplitude of all frequency components are obtained subsequently by means of reference signal construction, subtraction strategy and spectrum analysis. Finally, the precision frequencies of all components are obtained by an iterative procedure. Meanwhile, the precision amplitudes and initial phases of all components are also obtained. The simulation experiments of frequency estimation are carried on different conditions such as without noise and in different frequency interval, and the simulation results indicate that the proposed algorithm can effectively suppress the spectrum leakage influence and improve the frequency estimation accuracy of multi-tone real values sinusoid. In addition, the mean square errors of frequency estimation results are closer to the Cramer-Rao low Bound than those of other excellent algorithms.
Key words: frequency estimation; subtraction strategy; spectrum leakage; multi-tone real values sinusoid

Key words： frequency estimation subtraction strategy spectrum leakage multi-tone real values sinusoid

收稿日期: 2022-01-19 出版日期: 2022-10-15

引用本文:

陈鹏1,2，刘春华2，沈廷鳌3，乐开白2. 相减策略的含噪多频实信号频率估计算法[J]. 振动与冲击, 2022, 41(19): 152-156.
CHEN Peng1,2, LIU Chunhua2, SHEN Ting’ao3, YUE Kaibai2. Frequency estimation algorithm of multi-frequency real signals with noise based on Subtraction Strategy. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(19): 152-156.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I19/152

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