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This is a section for the parameter study of my thesis (basically: why and how I did what I did in the experiments). Currently, I have to choose the fit bandwidth and FFT lines combination for the experiment (for the parameter study, it is just giving an impulse for the generator, or hitting the metal specimen with a hammer). Investigations (actual measurement) say that with frequency resolution under 0.1 Hz, the spectrum obtained would be very squishy. For example, right below is 12800 FFT lines (or 12800 FFT bins) with different bandwidths (0.5, 1, 2, 5, 10 and 20 kHz) and different frequency resolutions (39.1, 78.1, 156.3, 390.6, 781.3 and 1562.5 mHz respectively)

enter image description here

The spectrum with 39.1 and 78.1 mHz frequency resolution (blue and orange) are very "squishy"...

Question 1: Why do we have such squishy spectrum?

For reference: this is non-squishy spectrum

enter image description here

Question 2: At low-frequency range (<50 Hz), smaller FFT bin shows peak better (more data point on the same range of frequency, thus easier to spot the peaks). But why at high-frequency, smaller FFT bins lead to lower peaks (at 300 and 330 Hz)?

Question 3: Is there a "critical point" for frequency resolution? Or the trade-off between frequency resolution vs spectral/time resolution? If yes, is there any source you can point towards for me, or is this more like a rule of thumb?

Thank you for your support (This question is also posted in Electrical engineering, and per the first comment, it is put here)

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What may explain why your spectrum is noisy is that you are computing it using a single burst of data. You will have to smooth it by averaging successive spectrums applied on your measurements. The number of samples that shall be used for the averaging have to be tuned depending on the speed of variation of your phenomena. After having done this, the other questions can be addressed more easily.

Best regards,

Mourad

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  • $\begingroup$ Thanks for your answer. The averaging has been done beforehand. Or the spectrum above is after doing the average (average over 9 samples over a scan point, or repeat a measurement 9 times and take the average). And yes, this is more or less "single burst" of data for my experiment (mechanical vibration with a laser scanner), when I hit the test specimen with an impulse $\endgroup$ – ComradeH Jan 5 at 9:25
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    $\begingroup$ Can you please provide more details about your experimental setup please ? How do you apply your filtering (you mentioned the variable bandwidth ), what is the sampling frequency you are using (1KHz I guess but just to make sure). What do you expect a particular frequency pattern in your signal? What is the resolution at which you would like to measure it ? $\endgroup$ – M.FAKHFAKH Jan 8 at 13:24
  • $\begingroup$ The digital used here is a FIR filter (comes with the software). It's a low-pass, with cut-off frequency at 2 kHz (I have tried various cut-off frequencies, and find out for some unknown reasons, there is no effect of the filter on the spectrum). The sampling frequency is 2.56 times the bandwidth (so 5.12 12.8 25.6 and 51.2 kHz). The current step is to investigate the effect of frequency resolution (from bandwidth and FFT lines) on the spectrum. The next step would be about window function. $\endgroup$ – ComradeH Jan 8 at 15:06
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    $\begingroup$ And what about the acquisition system ? do you know if there is any analog filtering performed before the acquisition ? There might be an aliasing occurring during your acquisition ( we don't know if the acquired signal's bandwidth respects the Shannon criteria). Consequently, if this issue is confirmed, this impacts your signal's integrity and shall be addressed as a first priority in your setup by adding an analog anti aliasing filtering before the acquisition. Also, can you provide spectrum graphs that cover all the frequencies (up to 20KHz so that we can see the filtering)? $\endgroup$ – M.FAKHFAKH Jan 9 at 10:33
  • $\begingroup$ Analog filter? Not sure, but there is a digital FIR filter (low-pass, set at 2kHz). The sampling frequency is set by the program to be 2.56 times higher than the bandwidth value, and I only interest up to 500 Hz only. The chart for up to 20 kHz is here link $\endgroup$ – ComradeH Jan 10 at 11:28

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