That data has a lot of discontinuities in the first derivative which will make this problem quite difficult. If, as you say, the data simply repeats (for many cycles?), you might try using a spline fit over several cycles. However, you have not shown even one complete cycle as your start and end values are very different.
You could also try smoothing the data (moving average, savitzky-golay?). It looks like relatively low sample rate relative to the higher frequencies in the data. How much of the higher frequency content do you need to retain?
Why do you need a fourier series? That may be the most pertinent question here. Sometimes, I notice that if I assume an approach to a problem initially, I get frustrated with making that approach work when, if I hadn't made that assumption in the first place and explored other options initially, I might have found the right approach sooner.
Look again at your data over a longer time period that actually shows the long term periodic behavior (I hope you have a more complete data set) and keep your mind open to other approaches than a fourier series.
So, after that ramble, please respond with answers to these questions and we might be able to help:
- Why do you think that you need a fourier series to fit the data?
- Can we really assume that the data is periodic over a longer time period?
- Do you have a longer dataset that shows the longer term periodic behavior?
If the answer to #3 above is yes, please attach the data to your original question. That would help a lot.
