matlab对矩阵自相关,自相关矩阵和互相关矩阵的matlab实现

自相关矩阵和互相关矩阵的matlab实现

一维实值x的自相关矩阵Rxx应为实对称的toeplitz矩阵，而一维实值信号x,y 的互相关矩阵Rxy为非对称的toeplitz阵，matlab提供的corrmtx产生的并非通常意义下的autocorrelation matrix

事实上，我们可以利用xcorr+toeplitz和corrmtx两种方法实现自相关阵Rxx 和互相关阵Rxy

一、Rxx

1)% implementation with xcorr and toeplitz

m= ;% dfine the time lag m+1, and m+1<=n;

n=length(x);%location of rxx(0);

rx=xcorr(x);%length of rx is 2*n-1;

Rxx=toeplitz(rx(n:n+m))/n;

2)%implementation with corrmtx

m= ;% dfine the time lag m+1,and m+1<=n

rx=corrmtx(x,m);

Rxx=rx'*rx;

二、Rxy

1)% implementation with xcorr and toeplitz

m= ;% dfine the time lag m+1, and m+1<=n;

n=max(length(x),length(y));location of rxy(0);

rxy=xcorr(x,y);%length of rxy is 2*n-1;

RR=toeplitz(rxy)/n;%RR is a (2*n-1)*(2*n-1) matrix

Rxy=RR(1:m,n:n+m);%the exact location of Rxy in RR;

2)% implementation with corrmtx

m= ;% dfine the time lag m+1, and m+1<=n;

rx=corrmtx(x,m);

ry=corrmtx(y,m);

Rxy=rx'*ry; %on the other hand, Ryx=Rxy'

上面的方法实现了自相关和互相关的有偏矩估计(实际是用实现卷积的前提