# Wiener filter with no WSS process

I'm trying to learn something more about Wiener Filters and I can't find anywhere what happens when I feed a Wiener Filter with a non WSS process. Could anyone give me an explanation or any book (specifically, which chapter/s) that explains that?

Thanks!

WSS: Wide Sense Stationary

• As you know, the Wiener filter is designed with respect to a given signal and noise statistics and will have the optimal performance. And as such it is a fixed filter for that particular case. If the input statistics changes during filtering, (that violating the WSS assumption) then either you should redesign your filter on the fly as an update process, or more appropriately enter to the amazing world of Adaptive Filtering . You shall begin with the Haykin's classical book "Adaptive Filter Theory" and also Widrow's book is highly recommended – Fat32 Aug 10 '16 at 14:55
• I'm reading Haykin's book and it's really nice, but I can't find the answer to my question. I mean, if the input of the filter (u(0), u(1), ...) is a non WSS process, what do I do? Of course I have to redesign the filter, but how? What conditions do I have to keep in mind? The filter model I'm using is from Haykin (I can't post an image here), in page 109 in the 5th edition – Euler Aug 10 '16 at 16:53
• so you haven't read yet the chapter on LMS adaptive filters? – Fat32 Aug 10 '16 at 19:08
• Of course I did! I also made a summary of that chapter. I did it in Spanish, but if you need it I can give it to you :). I read until chapter 10 because I didn't study yet Kalman filters. – Euler Aug 10 '16 at 19:17
• When the input process is not WSS, then your filter should adapt to its input's statistical characterisation, a property called as tracking. Those filters calles as LMS (being the simplest) will adopt their filter coefficients according to input characterisaiton and hence will try to provide optimal performance even when the input is not WSS. Of course tracking is not a perfect process and errors will be larger during. – Fat32 Aug 10 '16 at 19:18