A personal rule: in general, it can be useful to perform non-linear operations before linear ones.
Let me reformulate. If $f_i$ denote filters, and $s_i$ signals, should one do $f_0 \ast(s_1 .s_2)$ or $(f_1 \ast s_1)(f_2 \ast s_2)$? Without a better knowledge on the spectra of the signal, the nature of the noise and the numerically objective, I have no ...
In general you will need to multiply first and then low pass filter. You also have to make sure that your sample rate is high enough so the multiply doesn't create aliasing.
Let's look at a simple example: feed a 1kHz signal into a loudspeaker and measure current and voltage to determine the average (thermal) power with maybe a 100ms time constant. The ...
I think, the problem lies here:
scale back as a result of the FFT
clear non overlapping area in innput/output signal mic.
Why are you doing this? You are using a Hamming window with 50% overlap, summed up, this yields a constant one. If you delete the "non overlapping" part, you effectively change the window you are using to a weird "half hamming"...
I'm not sure what's you model is.
Let's say it is something like:
$$ y = H x + n $$
Now, using the Least Squares model is optimal (In the MSE sense) when $ n $ is AWGN (It is the linear optimal estimator if the noise is white).
So unless the noise in your model is colored, no gain by filtering the data before applying the Least Squares method.
Now, what ...