I'm trying to wrap my head around the proper use of a Wiener or error-prediction filter for filtering data. It seems to me that it is only a whitening filter, so how is it used when the data you want to recover isn't an AWGN signal?
For instance, I have a signal that has several distint interfering signals - I can see them on a PSD, but I don't know that they are a) stationary and b) what properties they have. I can use a method like Yule-Walker equations to recover the AR model for the whole signal, but in this case I only want to recover the model of the interfering signals, not the portion I want to recover.
I tried implementing an adaptive LMS notch filter, with the reference signal being a single sinewave, but this turned out to me much too narrow and didn't track frequency changes in the signal very well.
I guess basically my question is this, if I'm using an error prediction filter to filter real data, then how do I separate the data portion from the noise portion? In other words, I don't want to whiten the whole signal, only the noise portion. What am I missing?