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I am very new to this topic.

I ran a Fourier transform with the scipy fft function.

I than plotted the return values:

enter image description here

I am assuming the x-axis means how many cycles there are in all the data and y-values are the amplitudes at that number of cycles.

I have a time-series that I want to decompose into cycles. How do I use the information from this graph. The biggest amplitude is in the first example but I am assuming this doesn't matter.

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[Answer on original post] Do not hesitate to display the signal and your Fourier transform. It is important to check the soundness of using a Fourier transform, for instance with questions like:

  • is your signal long enough?
  • can we expect some stationarity?
  • should we first remove artifacts that could disturb interpretation, and how?

Here, I can only wonder on:

  • the x-axis index seems integer, with no apparent trace of the sampling frequency: keep track of it in the signal and Fourier representation:
  • the signal is not zero-average (first peak at 0), so it could be useful to remove the mean (zero-order average), and maybe higher order drifts (slope, or more) before going any further: those can affect the frequency interpretation a lot, for so many reasons
  • the shortness: with an index topping at 140, maybe the signal is less than 300 samples. maybe a little preprocessing could be useful: windowing, smoothing, etc.

Thus being said, on a restricted experience:

  • around indices 20 and 85, some local peak concentration may deserve further investigation.
  • it seems that the spectrum has some relatively fast "average decay" with frequencies.
  • yet, the fluctuations are somehow important, perhaps a consequence of insufficient preprocessing, or noise to harness.

Some additional information and updates on your post could be worthwhile.

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