基于中国余数定理及全相位理论的高精度频率估计算法研究
发布时间：2019-03-08 09:03
【摘要】：高频信号的频率估计与检测是雷达通信、声呐、地震监测、故障诊断乃至医学医疗等领域信号处理中至关重要的问题。但是根据奈奎斯特定律,若要精确估计实信号频率,至少要求一个信号周期内采样到2个以上样点,这必然要求采样速率大于等于两倍的待测高频信号的频率,因此耗费的硬件成本高。本文旨在解决在多路欠采样条件下(令信号频率为f0,要求采样速率fs2f0)高频信号频率的精确估计问题。为此,本文将古老的中国余数定理(Chinese Remainder Theorem,CRT)引入该领域中。基于中国余数定理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。因而首先需完成复信号精确频率估计工作,为此本论文引入原创的全相位FFT谱分析理论,借助apFFT/FFT相位差频谱校正法获得的精确频率余数,结合中国余数定理,实现了对复指数信号做精确频率估计,并将其成功应用于多普勒偏移估计中。为进一步将欠采样频率估计从复指数信号拓展到实余弦信号领域,本文提出两种基于不同频谱校正措施的余数筛选方法,精准地提取出余数定理所需的余数信息,实现了欠采样实余弦信号精细频率估计。其估计过程如下:(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(或者全相位快速傅里叶变换),并借助Candan估计器(或者全相位比值谱校正)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。数据模拟实验不但验证了该表达式的正确性,还反映了论文提出的方案具有高精度和高抗噪性能。
[Abstract]:Frequency estimation and detection of high frequency signals is an important problem in radar communication, sonar, seismic monitoring, fault diagnosis and even medical treatment. But according to Nyquist's law, in order to accurately estimate the real signal frequency, it is necessary to sample more than two samples in at least one signal cycle, which necessarily requires the frequency of the high frequency signal to be measured at a sampling rate greater than or equal to two times. As a result, the cost of hardware is high. The aim of this paper is to solve the problem of accurate estimation of the high frequency signal frequency under the condition of multi-channel undersampling (let the signal frequency be f _ 0, which requires the sampling rate fs2f0). In this paper, the ancient Chinese remainder theorem (Chinese Remainder Theorem,CRT) is introduced into this field. The estimation of signal frequency based on Chinese remainder theorem is a frontier problem in the fields of signal processing, electromagnetism and optics in recent years, but at present these studies are limited to rough frequency estimation of complex exponential signals. Therefore, it is necessary to complete the accurate frequency estimation of complex signals at first. Therefore, this paper introduces the original all-phase FFT spectrum analysis theory, with the help of the apFFT/FFT phase difference spectrum correction method to obtain the accurate frequency remainder, combined with the Chinese remainder theorem. The accurate frequency estimation of complex exponential signal is realized, and it is successfully applied to Doppler migration estimation. In order to extend the undersampling frequency estimation from the complex exponential signal to the real cosine signal, two methods of residual selection based on different spectral correction measures are proposed in this paper, which can accurately extract the remainder information required by the remainder theorem. The precision frequency estimation of undersampled real cosine signal is realized. The estimation process is as follows: (1) Zero-crossing detection of the high-frequency cosine waveform is carried out to determine the phase information of the signal; (2) Fast Fourier transform (or all-phase Fast Fourier transform) is performed for each undersampled signal, and frequency correction is performed for each spectral peak value by means of Candan estimator (or all-phase ratio spectrum correction) to obtain high-precision residual estimation. Based on this, the frequency offset is calculated for phase correction. (3) using the proposed phase feature classification method to select the corrected remainder, (4) to substitute the filtered frequency remainder into the closed form of Chinese remainder theorem to obtain the high-precision estimation of the original signal frequency. In addition, the theoretical expression of the variance of frequency estimation is also derived in this paper. The data simulation experiment not only verifies the correctness of the expression, but also reflects the high precision and anti-noise performance of the proposed scheme.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.23
本文编号：2436649
[Abstract]:Frequency estimation and detection of high frequency signals is an important problem in radar communication, sonar, seismic monitoring, fault diagnosis and even medical treatment. But according to Nyquist's law, in order to accurately estimate the real signal frequency, it is necessary to sample more than two samples in at least one signal cycle, which necessarily requires the frequency of the high frequency signal to be measured at a sampling rate greater than or equal to two times. As a result, the cost of hardware is high. The aim of this paper is to solve the problem of accurate estimation of the high frequency signal frequency under the condition of multi-channel undersampling (let the signal frequency be f _ 0, which requires the sampling rate fs2f0). In this paper, the ancient Chinese remainder theorem (Chinese Remainder Theorem,CRT) is introduced into this field. The estimation of signal frequency based on Chinese remainder theorem is a frontier problem in the fields of signal processing, electromagnetism and optics in recent years, but at present these studies are limited to rough frequency estimation of complex exponential signals. Therefore, it is necessary to complete the accurate frequency estimation of complex signals at first. Therefore, this paper introduces the original all-phase FFT spectrum analysis theory, with the help of the apFFT/FFT phase difference spectrum correction method to obtain the accurate frequency remainder, combined with the Chinese remainder theorem. The accurate frequency estimation of complex exponential signal is realized, and it is successfully applied to Doppler migration estimation. In order to extend the undersampling frequency estimation from the complex exponential signal to the real cosine signal, two methods of residual selection based on different spectral correction measures are proposed in this paper, which can accurately extract the remainder information required by the remainder theorem. The precision frequency estimation of undersampled real cosine signal is realized. The estimation process is as follows: (1) Zero-crossing detection of the high-frequency cosine waveform is carried out to determine the phase information of the signal; (2) Fast Fourier transform (or all-phase Fast Fourier transform) is performed for each undersampled signal, and frequency correction is performed for each spectral peak value by means of Candan estimator (or all-phase ratio spectrum correction) to obtain high-precision residual estimation. Based on this, the frequency offset is calculated for phase correction. (3) using the proposed phase feature classification method to select the corrected remainder, (4) to substitute the filtered frequency remainder into the closed form of Chinese remainder theorem to obtain the high-precision estimation of the original signal frequency. In addition, the theoretical expression of the variance of frequency estimation is also derived in this paper. The data simulation experiment not only verifies the correctness of the expression, but also reflects the high precision and anti-noise performance of the proposed scheme.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.23
【引证文献】
相关硕士学位论文 前1条
1 黄励勤;电机转子全自动动平衡机的研制与开发[D];华南理工大学;2016年
，本文编号：2436649
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