单频复正弦信号频率估计

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单频复正弦信号频率估计

摘要：频率估计是数字信号处理的重要内容，对淹没在噪声中的正弦波信号进行频率估计是信号处理的一个经典课题。目前，高精度频率估计己经成功应用于雷达探测、声纳地震监测、桥梁振动检测以及电子通信技术中，因此，研究高精度频率估计算法，具有重要的理论意和应用价值。

本文对于高斯白噪声中单频复正弦信号的频率估计,对常用的几种频率估计方法进行了回顾，提出了一种对复加性高斯白噪声环境下的复正弦信号的频率进行估计的迭代方法。该方法在Kay提出的相位加权平均（WPA）方法的基础上引入迭代的思想，只需要通过少数几次迭代就可克服WPA方法中信噪比门限随所估计的复正弦信号频率的增大而升高的缺点，从而大大提升估计性能。新的迭代方法的估计范围为整个[ , )区间，且在这整个估计范围内，新的迭代方法都能得到基本相同的较低信噪比门限。仿真实验的结果验证了新的迭代方法对WPA方法及WNLP方法的性能提升，说明了该方法的优越性。

关键词 复正弦信号，频率估计，信噪比门限，相位加权平均算法，迭代算法，matlab

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Abstract：Frequency estimation is an important part of digital signal processing, and submerged in the noise of the sine wave signal of frequency estimation is a classic signal processing tasks.Currently, high-precision frequency estimation has been successfully applied to radar, sonar, seismic monitoring, bridge vibration testing and electronic communications, therefore, of high accuracy frequency estimation algorithm, has important theoretical significance and application value.

This white Gaussian noise for a single complex sinusoid of frequency estimation, frequency estimation of several commonly used methods were reviewed, a pair of complex additive white Gaussian noise environment of the complex sinusoidal signal to estimate the frequency of iterative method. The method proposed phase-weighted average Kay (WPA) method based on the introduction of iterative thinking, only a few times through the iteration method can overcome the WPA with the estimated signal to noise ratio threshold of the complex sinusoidal signal frequency increases increased shortcomings, which greatly enhance the estimation performance. New iteration method for the entire range of the estimated range, and estimates in the context of the whole, the new iteration method can be basically the same low signal to noise ratio threshold. Simulation results verify the new method and iterative method WPA performance WNLP method shows the superiority of the method.

Kaywords:Complex sinusoid,Frequency estimation,SNR threshold,Phase weighted average algorithm，Iterative algorithm，matlab

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目录

1. 引言.............................................................................................................................................. 1 2. 频率估计的研究综述相关算法回顾 .......................................................................................... 3

2.1 最大似然估计法 ................................................................................................................ 3 2.2 双线幅度法(Rife法) ......................................................................................................... 4 2.3 M-Rife算法(修正Rife算法) ............................................................................................ 6 2.4 Quinn 频率估计方法 ....................................................................................................... 10 2.5 分段FFT法测频 ............................................................................................................. 14 2.6 相关结论 .......................................................................................................................... 16 3. 频率估计的相位加权平均算法及其迭代方法 ........................................................................ 17

3.1 相位加权平均法 .............................................................................................................. 17 3.2 迭代方法 .......................................................................................................................... 19

3.2.1 信号模型 ............................................................................................................... 19 3.2.2 WPA方法及其问题 ........................................................................................... 20 3.3.3 频率估计的迭代方法 ........................................................................................... 21

4. 性能对比及计算机模拟结果 .................................................................................................... 25 5. 结论............................................................................................................................................ 29

致谢......................................................................................................................................... 30 参考文献: ............................................................................................................................... 31 附录......................................................................................................................................... 33

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1. 引言

频率是参量估计中的一个重要物理量。高斯白噪声中复正弦信号进行频率估计是对高斯白噪声中复正弦信号进行频率估计是一个广泛研究的重要课题。要高精度和高速度测量信号频率必须要有好的频率估计方法,一种好的频率估计方法,在在雷达、通信、地球物理、通信对抗侦察及生物医学信号处理等领域都能占据更大优势。频率估计方法繁多,在实际信号处理中采取何种方法,是经常要遇到的问题。

参考文献[1]中给出在高斯白噪声中对正弦波信号进行频率估计的最大似然估计(ML)算法,该算法估计误差达到克拉美-罗限(CRLB) ,因此是最优估计. 但是ML算法需要进行一维搜索,计算量太大,无法进行实时处理. 文献[2][3]利用信号频谱的最大两根谱线进行插值对频率进行估计. 文献[4]对噪声背景中的插值FFT方法估计正弦波频率的精度进行研究,指出当信号真实频率与DFT 量化频率差为某一范围时Rife 算法精度不高. 文献[5]提出相位平均算 …… 此处隐藏：4337字，全部文档内容请下载后查看。喜欢就下载吧 ……