The weights are not dependent on your input and output signals to your unknown system, but are dependent on the filter characterists you are estimating. If you want to check the time-varying properties of RLS you are better either varying the cutoff of that unknown filter or generating a system from an FIR model and change its weights. As long as the input and out are measurable and are persistantly exciting then you will get the same result. If you put a sine wave as the input then you may well get false results. (unless you sweep it)
