信号的自相关、互相关和协方差

信号的相关矩阵或协方差矩阵在系统识别中扮演着重要角色。事实上，对于一个LTI随机系统，其输出序列的二阶统计量完全可以确定该系统。

定义

 

 

 

 

 

 

互相关和协方差

 

对于均值为0的白噪声序列，二者形式是一致的。

Matlab计算

matlab中的相关命令：

% 协方差矩阵

data_cov = cov((data));

 

%信号自相关
autocorr(data, 1023)

 

% 互相关系数

R = corrcoef(data);

 

% 互功率谱密度（互功率谱密度与信号的互相关函数具有傅里叶变换关系）

pxy = cpsd(x,y,window,noverlap,nfft)

 

% Cross-correlation 互相关or自相关

[a,b]=xcorr(x,'unbiased');

[a,b]=xcorr(x,y,'unbiased');

 

scaleopt — Normalization option
'none' (default) | 'biased' | 'unbiased' | 'coeff'

 

 

 

 

returns the cross-correlation of two discrete-time sequences, x and y.

Cross-correlation measures the similarity between x and shifted (lagged) copies of y as a function of the lag.

If x and y have different lengths, the function appends zeros at the end of the shorter vector so it has the same length, N, as the other.

 

 

 

autocorr和xcorr有什么不一样的？

 

 

% 与xcorr类似的还有互协方差xcov

c = xcov(x,y)

c = xcov(x)

 returns the cross-covariance of two discrete-time sequences, x and y.

Cross-covariance measures the similarity between x and shifted (lagged) copies of y as a function of the lag.

If x and y have different lengths, the function appends zeros at the end of the shorter vector so it has the same length as the other.

 

 

 

 

 

 

 

https://blog.csdn.net/jonathanlin2008/article/details/6566802

https://www.cnblogs.com/maxwell-maxwill/p/12146919.html

https://blog.csdn.net/scuthanman/article/details/5588138