检测技术与信号处理（十五）

根据上次的学习，我们学习了信号的互相关函数，接下来我们接着上次的讲解，和大家学习一下相关函数估计并简单介绍一下功率谱。

According to the previous study, we learned the cross-correlation function of the signal. Next, we will continue with the previous explanation, and learn about the correlation function estimation and briefly introduce the power spectrum.

相关函数估计

对于周期信号，可用一个周期内的观察值的平均值代表整个过程的平均值。而对于随机信号，可用有限时间的样本记录所求得得相关函数值来作为随机信号相关函数的估计，即

For periodic signals, the average value of observations in a period can be used to represent the average value of the entire process. For random signals, the correlation function value obtained from the sample record of a finite time can be used as the estimation of the correlation function of the random signal, namely

而对于有限个序列点N得数字信号的相关函数估计，可写成

And for a finite number of sequence points N to obtain the correlation function estimation of the digital signal, it can be written as

之后简单介绍一下功率谱作用分析，信号的时域描述反映了信号幅值随时间变化得特征，相关分析从时域为在噪声背景下提取有用信息提供了手段，并且信号的频域的描述反映了信号的频率提供了信号的频率结构和各频率成分的幅值大小，功率谱密度函数、相关函数、倒谱分析则从频域为研究平稳随机过程提供了重要方法。

Then briefly introduce the analysis of the power spectrum effect. The time domain description of the signal reflects the characteristics of the signal amplitude over time. The correlation analysis provides a means from the time domain to extract useful information under the background of noise, and the frequency domain description of the signal reflects The frequency of the signal provides the frequency structure of the signal and the amplitude of each frequency component. The power spectrum density function, correlation function, and cepstrum analysis provide important methods for studying stationary random processes in the frequency domain.

首先介绍一下自功率密度函数：x(t)是零均值的随机信号（若x(t)是非零均值的，可以通过适当处理使其均值为0），并假定x(t)中没有周期分量，则；

First introduce the self-power density function: x(t) is a random signal with zero mean value (if x(t) is a non-zero mean value, it can be processed to make its mean value 0), and it is assumed that there is no periodic component in x(t) ,but;

将自相关函数的傅里叶变换

Fourier transform of autocorrelation function

定义为其自功率谱密度函数，简称为自功率谱或自谱。据傅里叶逆变换，有

Defined as its self-power spectral density function, referred to as self-power spectrum or self-spectrum for short. According to the inverse Fourier transform, there are

相信大家通过PPT上的解说已经对相关函数估计有了一定的了解。下周五我为大家介绍功率谱应用。

I believe that everyone has a certain understanding of the correlation function estimation through the explanation on the PPT. I will introduce the power spectrum application to you next Friday.

参考资料：

文字：重庆邮电大学郑佳老师检测技术与信号处理PPT；

图片：百度；

翻译：GooGle翻译.

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