Reverse engineering a digital filter I have 2 simultaneous signals that both are designed to measure eye movements.
They are sampled at 250 Hz.
We have 12 subject recordings.
For 3 stable periods in each subject, we choose 256 points and did an FFT.
Prior to the FFT, the data were mean-centered and detrended with a 2nd
order polynomial.  They were also windowed with a Hann window. 
We are focused on the magnitude spectra plots.
We have a total of 12 X 3 = 36 magnitude spectra, which we average.
These averages are shown in the attached figure. 



My hypothesis is that the second signal is a low-pass filtered version of
the first.  The filter has ringing in the passband.

I want to design a digital filter that I would apply to signal 1 that,
after fft, analyses would produce a magnitude spectra like that of 
signal 2.

How would I go about this?
Signal 1 was an average of a left and right signal and signal 2 was a binocular signal.

I followed the suggestion of MBaz, and computed the frequency response of the filter for each segment (N = 3) for each subject (N=12).  Then I averaged the frequency responses of the filters. Here is the result:


MBaz and Matt: Thank you so much for solving my problem.
Matt, it looks close to your filter.
Lee