How to interpret Fourier transform?

Question

I am very new to this topic.

I ran a Fourier transform with the scipy fft function.

I than plotted the return values:

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.

Answer 1

[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.