Autocorrelation Matrix from a vector

Question

xplore29 2012-9-26

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/49172-autocorrelation-matrix-from-a-vector

I have observations of a noisy channel and i form a vector y of length n from those observations. I need to compute the autocorrelation matrix from this vector y which should be just the outer product y*y' i-e E[y*y']=y*y'. This matrix is a rank=1 nxn matrix. Is this correct?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Wayne King 2012-9-26

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/49172-autocorrelation-matrix-from-a-vector#answer_60095

编辑：Wayne King 2012-9-26

在 MATLAB Online 中打开

No, that is not correct. The way you are doing it is not giving the autocorrelation matrix. For one thing your matrix is not going to be Toeplitz.

For example:

    x = randn(10,1);
    rxx = x*x';

Note the above, rxx, is not Toeplitz.

But

[xc,lags] = xcorr(x,x,9,'biased');
r = xc(10:end);
rxx = toeplitz(r,conj(r)); % the conj() of course here is not needed

Now, rxx is Toeplitz and not that the autocorrelation matrix has full column rank.

rank(rxx)

Or you could do:

    X = fft(x,2^nextpow2(2*size(x,1)-1));
    R = ifft(abs(X).^2);
    m = length(x);
    R = R./m; % Biased autocorrelation estimate
    rxx = toeplitz(R(1:length(x)),conj(R(1:length(x))));