# 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) -> (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) -> 3: Rectification (abs(xi)^2) -> 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...

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.
• Any chance you can attach the signal plot as well? Mar 25 '20 at 10:55
• Hm, why would you first in 1: cut off anything above 2000 Hz, then in 2: cut off anything below 8750 Hz? That very much sounds like a design mistake. If your low-pass filters are good, you don't have any signal after that. Mar 25 '20 at 10:58
• The 25.6Hz in your question is a typo, correct? It should be 25.6kHz based on your previous questions.. Mar 25 '20 at 11:44
• @DSPNovice added some more plots. Let me know if you would like to see more. Mar 25 '20 at 14:38
• @MarcusMüller I updated the process. The optimal bandwidth is around 9000 Hz from the spectral kurtosis. Mar 25 '20 at 14:40

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.

• True, there seems to be a bin at around 25 Hz and another at 50 Hz probably caused by the rectification process.
– Ben
Mar 25 '20 at 13:34
• Wouldn't the rectification step (I am doing the abs value and then raising to the power of 2) move the high frequency resonances to lower frequencies abnds? I'm looking to perform an enveloping process in my case. What is an alternative to the rectification step? (I remember you mentioned the issue with just performing the abs value in another answer). Mar 25 '20 at 14:49
• I had a major typo, I meant to write step 1: Highpass (2000 Hz) Mar 25 '20 at 14:55

Maybe you should average your FFT over time to enhance you signal's SNR, you may then be able to see a spectrum that fits your expectations. It also seems that your signal is filtered around 420 Hz. Unless this is your initial signal's bandwidth, your filtering may not have been applied correctly.