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Estimating a Wiener filter manually in Matlab 
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#1
Jan1513, 02:25 PM

P: 11

Hi all!
Problem: 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: H(s)=1/Fi(s)*[Sx(s)/Fi(s)]_{L} I know that: Fi(s)Fi(s)=Sx(s)+Sn(s) 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). Question: 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: [Sx(s)/Fi(s)]_{L} I have Sx(s) and Fi(s), but my question is how do I determine the transfer function of the noncausal 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. Gonçalo 


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