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I have a system which consists of individual pulses grouped in trains.

  • The trains have a frequency of 10 Hz, with a timing precision of sub ns.
  • The pulses have a frequency of 2.2 MHz with a timing precision of sub ps. The train consists of 100-1000 pulses.

I would like to do a spectrogram in the range 0.1 - 100 Hz. Up to 5 Hz its trivial. I simply take the average of the train and still have the Nyquist theorem fullfilled. However I see a lot of signal which could come from aliasing. Is there a possibility to use the 5 order of magnitude faster signal from the individual pulses to gain anything useful here? I have a maximum of 25d of data. But I would ideally like to do a spectrogram, meaning it would be great to stay within about an hour of data (e.g 36k trains)

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  • $\begingroup$ What sort of information are you expecting to extract from the spectrogram? $\endgroup$ – A_A Oct 22 '19 at 12:04
  • $\begingroup$ @A_A, I have three distinct periodic signals (<5Hz) where one of which is constant. My goal is determine their real frequency and pinpoint them in time. I hope this will help my to find its source within a big industrial system. (pump switching on / pressure or temperature change / load change / ...). The final goal is then obviously mitigating said effect from the source. $\endgroup$ – magu_ Oct 22 '19 at 12:18
  • $\begingroup$ What I was hinting at is the kind of quantities you are trying to derive off of the spectrogram because you might be able to extract them much simpler and quicker by capturing things like pulse onset timestamps or even pulse widths (?). $\endgroup$ – A_A Oct 22 '19 at 12:38
  • $\begingroup$ @A_A, I'm afraid I can't follow. How would the pulse width (in the spectrum or the time domain?) help me getting higher frequency signal components? $\endgroup$ – magu_ Oct 22 '19 at 14:05
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The first step is to low pass filter the signal with 100Hz cutoff and then resample everything at 200Hz. This doesn't change the spectrum in the 0-100Hz range. Therefore, it's not possible to gain anything of use from the faster signals.

The 0-100Hz spectrum will be the same as if there were a single 45-450μs pulse occuring at 10Hz. There will peaks at multiples of 10Hz (harmonics) and the maximum will be the 10Hz peak itself.

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