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侯朝焕, 武振东. 宽带相关噪声中窄带信号的高分辨率谱估计法[J]. 声学学报, 1981, 6(6): 337-347. DOI: 10.15949/j.cnki.0371-0025.1981.06.001
引用本文: 侯朝焕, 武振东. 宽带相关噪声中窄带信号的高分辨率谱估计法[J]. 声学学报, 1981, 6(6): 337-347. DOI: 10.15949/j.cnki.0371-0025.1981.06.001
HOU Chao-huan, WU Zhen-dong. HIGH RESOLUTION SPECTRAL ANALYSIS OF A NARROW-BAND SIGNAL IN THE BROAD-BAND CORRELATED NOISE[J]. ACTA ACUSTICA, 1981, 6(6): 337-347. DOI: 10.15949/j.cnki.0371-0025.1981.06.001
Citation: HOU Chao-huan, WU Zhen-dong. HIGH RESOLUTION SPECTRAL ANALYSIS OF A NARROW-BAND SIGNAL IN THE BROAD-BAND CORRELATED NOISE[J]. ACTA ACUSTICA, 1981, 6(6): 337-347. DOI: 10.15949/j.cnki.0371-0025.1981.06.001

宽带相关噪声中窄带信号的高分辨率谱估计法

HIGH RESOLUTION SPECTRAL ANALYSIS OF A NARROW-BAND SIGNAL IN THE BROAD-BAND CORRELATED NOISE

  • 摘要: 本文提出在宽带相关噪声中,提取窄带信号谱分量的一种高分辨率谱分析方法.基于宽带噪声的相关半径远小于窄带信号分量的相关半径,在输入时间过程的相关函数的大延时部份,宽带噪声的影响已相当弱.因而可利用测量到的大延时部份的相关函数来估计窄带信号的谱分量.本文首先用复指数近似方法,将大延时相关函数内插,得到窄带信号分量的小延时部份的相关函数的估计值.利用大延时相关函数的测量值,加上小延时相关函数的估计值,构成完整的相关函数。其次,按最大熵方法外推相关函数,得到高阶的最大熵预测系数,由此得到窄带信号分量的频率、功率和带宽的精确估计.为了达到高分辨率而采用高阶相关矩阵,谱估计的运算量十分大.本文提出节省运算量的有效方法,可避免同时解出全部谱分量,而仅选出功率较大的谱分量来对其频率作精确估计.最后,以宽带相关噪声中的多个正弦信号为例,给出了线谱分量的各参量估计的计算机模拟结果.本文提出方法的谱分辨率较常规谱分析法的谱分辨率提高很多倍。

     

    Abstract: In this paper, a high resolution technique for detecting the presence of frequency components of a narrow-band signal in the broad-band correlated noise is examined. It is based on the fact that the correlation interval of a broad-band noise is much smaller than that of a narrow-band signal. When the time lag of the autocorrelation function of the input is larger than the correlation interval of the broad-band noise, the effect of broad-band noise is negligible. Therefore, the measured autocorrelation function of large time lag can be used to estimate the frequency components of the narrow-band signal. The basic procedures of the estimation is presented in the paper. Firstly, the autocorrelation function of large time lag is interpolated to the section of small time lag with complex exponential algorithm and the estimation of the autocorrelation function of small time lag for a narrow-band signal is obtained. The whole autocorrelation function is thus constructed from the measured section of large time lag and the estimated section of small time lag. Secondly, the autocorrelation function is extrapolated by using the maximum entropy method to obtain the weighting coefficients of the high-order prediction filter. Then the frequency, power and bandwidth of the components of the narrow-band signal can be estimated accurately. In order to yield high resolution, the high-order autocorrelation matrix is used, the number of the operations for the estimation of frequency and power is tremendous. An efficient method for significantly reducing the number of operation is suggested. In this method, frequency components of stronger power, instead of all components, are used to estimate the frequency accurately and the power approximately. Finally, a series of computer experiments is performed. As an example, the results for the parameter estimation of the line spectrum of sinusoids in broad-band noise are given. The computer simulation shows that spectral resolution of new method presented in this paper is higher than conventional spectral analysis.

     

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