How to compute Wiener equation?

Question

RAFAEL ACOSTA 2021-5-12

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https://ww2.mathworks.cn/matlabcentral/answers/828680-how-to-compute-wiener-equation

回答： Pratyush Roy 2021-5-17

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!

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Answer 1

Pratyush Roy 2021-5-17

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https://ww2.mathworks.cn/matlabcentral/answers/828680-how-to-compute-wiener-equation#answer_701473

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!