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I have a frequency spectrum of a particular phenomenon (it is the Fast Fourier Transform of the stress response in iron to an induced strain). In short, the stress oscillates and I wish to analyse the frequency of the oscillations.enter image description here

A typical frequency plot looks like the attached

I want to represent these frequencies as a single number, some sort of "characteristic frequency". I can obviously choose the frequency with the maximum amplitude, OR some sort of weighted "average".

I can calculate the weighted arithmetic, geometric and harmonic mean and of course, these averages vary in magnitude.

The question is, of these three averages, which is more "correct" or rather, more "representative" for this sort of data? And why?

kind regards W

William White
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  • (yes, I have spelled amplitude wrong!) – William White Sep 05 '18 at 20:19
  • You've plotted the frequency on a logarithmic scale, so it makes sense to use the geometric mean. – mr_e_man Sep 05 '18 at 20:46
  • can you explain why? (the reason frequency is on the log scale is because most of the "action" happens in a small frequency range (low kHz) but the entire spectrum goes up to 1GHz. Plotting on a linear scale shows nothing, But I could plot just the KHz frequencies on a linear scale) – William White Sep 05 '18 at 20:50
  • Plot Log frequency between $10^4-10^8$ Hz.Root Mean Square value can be found for such a linearized plot. – Narasimham Sep 05 '18 at 21:42
  • I'm voting to close this question as off-topic because "which average is more representative?" depends on the use to which you put that statistic. It does not have a mathematical answer. – Ethan Bolker Sep 06 '18 at 00:07
  • I would use a peak-finding routine, because it will give you a reasonable number that is not too sensitive to local noise, but will capture the overall shape of your FFT. What is your original sampling rate? And what is $\Delta f,$ your frequency bin size? You'll want to key off of those to get the window size for your peak-finder. You also might consider applying a median filter first. – Adrian Keister Sep 06 '18 at 00:36
  • Ethan - I have to strongly disagree: I have given the context of what the data represents. Different averages are better for different data sets; and I wish to hear from stats experts as to what sort of average is best to describe this data. Please be more helpful and less dismissive and remove your unhelpful vote. These forums are to help people - you are working to do the opposite. – William White Sep 06 '18 at 14:40
  • Adrian - sampling rate is 2GHz. Δf is 8kHz. I have also previously done the things you recommend. I suppose the crux of my question is what is bothering Ethan - I know different means are used for different data sets, for example geometric means are used for average speeds etc; so I was wondering what sort of mean is best suited - i.e. a good physical representation - for oscillating signals. – William White Sep 06 '18 at 14:46

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