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Signals contain both transient and stabilizing processes. In the transient process, the signal exhibits oscillatory behavior with damping. Is there some efficient algorithms to extract the frequency? I want extract the frequency to do system diagnosis. If not, I can also accept some inefficient algorithms. The bandwidth of the current sensor is several hundred MHz, and the sampling period is 0.4ns in order to capture the transient process.

Measured current signal

However, the damping behavior is not monoton, as shown in the following figure. Therefore, I am interested in the dominated frequency.

Another signal whose damping behavior is not clear

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  • $\begingroup$ Are you familiar with time-frequency domains such as the Short Time Fourier Transform? $\endgroup$ Commented Oct 5, 2023 at 19:35
  • $\begingroup$ I am not familiar with STFT. do you think it would solve the problem? $\endgroup$ Commented Oct 6, 2023 at 8:09
  • $\begingroup$ Yes it would. Why don’t you try and see if Hilmar’s “dirty and quick” method fits your needs, and if it doesn’t, come back and I’ll be happy to help with this. $\endgroup$ Commented Oct 6, 2023 at 15:02

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The easiest "quick and dirty" way of determining the frequency is to simply measure the time distance of the first and last maximum (or minimum) that you can reliably determine and divide by the number of periods in between.

I did this and it looks like it's ringing mostly at 2 MHz.

A more precise method would be to cut out a segment (as you already have done) and do an FFT on it. Determine the peak frequency. For these type of events a rectangular window should be fine. You can zero pad to increase frequency resolution.

It would help if you have some idea of the physical system that is creating the response. It looks like a 2nd order lowpass filter with pretty high Q. If that's a good assumption, you can try to do a parametric fit of the curve. Below is a starting point

enter image description here

However, the damping behavior is not monoton, as shown in the following figure.

I think you are misinterpreting what's happening here. This looks very much like a system reacting to noise spikes. Each spike triggers the impulse response of the system which would indeed be decreasing monotonically (mostly).

What you see here is most likely a double spike, i.e. two events that partially overlap. The overlap is a tricky to deal with, so if you have enough "single" events, I would discard the "doubles".

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  • $\begingroup$ Thank you very much, it is very helpful $\endgroup$ Commented Oct 6, 2023 at 7:59
  • $\begingroup$ Is it possible to perform an FFT on a signal that is not a periodic signal but a signal with damped oscillations? $\endgroup$ Commented Oct 6, 2023 at 8:01
  • $\begingroup$ for the curve fitting, do you mean that i can use the A* exp(-at)*sin(omega*t+phase_offset) $\endgroup$ Commented Oct 6, 2023 at 8:05
  • $\begingroup$ You can a perform an FFT on every signal. Something that has oscillations will have some peaks. Curve meeting means that you use a model "whatever the physics of the system are". But yes, a exponentially decaying sine wave is a good starting point from the looks of it. $\endgroup$ Commented Oct 6, 2023 at 11:41

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