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Estimating a Wiener filter manually in Matlab

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Jan15-13, 02:25 PM
P: 11
Hi all!

I am currently trying to calculate a Wiener filter for a stochastic system. The model is an ARX with determined parameters.

Where I am:
I have access to the transfer functions of the ARX model.
I need to calculate the optimal causal filter:

I know that:
where Sx(s) is the power spectral density of the output signal and Sn(s) is the power spectral density of the aditive noise. To find Sx and Sn I found the square root of the absolute value of the transfer functions of the model and the noise filter respectively, in the jω domain.

I have the whitening filter (1/Fi(s)), I determined Fi(s) by taking out all poles and zeros on the right plane of Fi(s)Fi(-s).

Is the bode diagram of the whitening filter supposed to be the symetric, relative to magnitude, of the bode diagram of the noise filter of the model?

Now I have to determine:
I have Sx(s) and Fi(-s), but my question is how do I determine the transfer function of the non-causal part only? I know I could use partial fraction expansion by hand but my Sx(s) and Sn(s) have 12th order polynomials so I will certainly not go that way.

Please help.
Thank you.

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