FFT looking messy after filtering process I have a vibration signal (25.6 kHz)  which has been through the following filters:

1: highpass (2000 Hz) -&gt; (I'm not interesten in the harmonics of the system. I then perform spectral kurtosis to find the optimal bandpass bandwidth.)
 2: Bandpass (8750 Hz,9250 Hz) -&gt;
 3: Rectification (abs(xi)^2) -&gt; 
 4.Lowpass (2000 Hz)

The fft of the final signal looks like this:


The Bandpass filter bandwidth and center frequency was selected based on the kurtogram of signal after initial lowpass.

I am no expert in signal processing- does the FFT look "correct"? It seems odd that the amplitudes rarely go below 0.05...

Updates

The original signal (25.6 kHz):


Zoomed in in original signal (25.6 kHz):


Final signal in time domain:


FFT of original signal (before step 1) 


Objective of project:


To look for any fault development in the early stages of a gearbox fault on a wind turbine. I have signal data 412 days, in the form of 412 10-second intervals.
Want to extract features from time and freq. domain and cluster the 412 intervals, to see if there is a pattern.
If your description is correct, you are seeing noise.

After step 1, everything above 2 kHz should be gone. After your band-bass everything below 8750 Hz is gone, so you basically end up with a null set. Since your filters are not infinitely steep there is still something non-zero left over but it's mostly going to be noise and very poorly defined.

Rectification is also a highly non-linear operation, so chances are you also going to get some aliasing in there as well.