基于中国余数定理的欠采样下余弦信号的频率估计

发布时间：2018-11-21 09:46

【摘要】：基于中国余数定理的重构算法的信号频率估计是近年来信号处理、电磁学以及光学等领域的前沿问题,但目前这些研究仅限于对复指数信号做粗略频率估计.因而,本文把基于中国余数定理的频率估计从复指数信号粗估计拓展到实余弦信号精细估计领域,其所提出的估计方案处理过程如下:1)对高频余弦波形进行过零点检测,确定信号的相位信息;2)对各路欠采样信号做快速傅里叶变换,并借助Candan估计器对各路谱峰值做频率校正以获取高精度余数估计,基于此算出频偏值以做相位校正;3)用提出的基于相位特征分类方法对校正得到的余数做筛选;4)将筛选出的频率余数代入闭合形式的中国余数定理得到原信号频率的高精度估计.此外,本文还推导出了频率估计方差的理论表达式.数据模拟实验验证了该表达式的正确性,实验结果还反映了本文提出的方案具有高精度和高抗噪性能.
[Abstract]:The signal frequency estimation based on the Chinese remainder theorem is a frontier problem in the fields of signal processing, electromagnetics and optics in recent years, but at present these researches are limited to the rough frequency estimation of complex exponential signals. Therefore, the frequency estimation based on the Chinese remainder theorem is extended from the coarse estimation of complex exponential signals to the precise estimation of real cosine signals. The processing process of the proposed estimation scheme is as follows: 1) the zero-crossing detection of high frequency cosine waveforms is carried out. Determining the phase information of the signal; 2) Fast Fourier transform (FFT) is performed for each under-sampled signal, and frequency correction of the peak value of each spectrum is made by using Candan estimator to obtain high-precision residual estimation. Based on this, the frequency offset value is calculated to make phase correction; 3) the proposed method based on phase feature classification is used to screen the corrected remainder; 4) the frequency residue is replaced by the closed Chinese remainder theorem to obtain the high accuracy estimation of the original signal frequency. In addition, the theoretical expression of frequency estimation variance is derived. The correctness of the expression is verified by the data simulation experiment, and the experimental results show that the proposed scheme has high accuracy and high anti-noise performance.
【作者单位】：天津大学电子信息工程学院;
【基金】：天津市应用基础及前沿技术研究计划重点项目(批准号:10JCZDJC16100) 国家自然科学基金(批准号:61271322)资助的课题~~
【分类号】：TN911.23

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