How to compute Wiener equation?

I have this signal: w=(1,-0.5) and other signal d=(1,0)

I am trying to solve the Wiener normal equation on MATLAB, that is:

where is the autocorrelation matrix.. is the vector that I want to find and is the xcorr between w and d.

I am using xcorr(w) and xcorr(w,d) to solve equation (1), however, I am not getting a matrix just a vector. Could someone help me? How can I transform the xcorr(w) vector into a matrix?

Thanks in advance!

Answer 1

[Pratyush Roy]

Hi Rafael,

The autocorrelation matrix obtained from the data while using Weiner filtering is a symmetric Toeplitz Matrix. If the autocorrelation vector is available, it can be converted to a symmetric Toeplitz matrix using the toeplitz method.

Hope this helps!