# special functions – Microfluctuations analysis and Power spectrum

You don’t have enough points to work out a power spectrum. A power spectrum is an average of many spectra. You do have enough points to work out a Fourier spectrum.

First I convert your data to Mathematic format. We prefer you post in Mathematica format since it saves us extra work and you are more likely to get an answer.

``````data = {0.627896`, 0.205004`, 0.259237`, 1.059125`, 0.832184`,
0.587992`, 0.565537`, 0.527323`, 0.460228`, 0.471958`, 0.26696`,
0.75367`, 0.892273`, 0.789401`, 1.089945`, 0.579791`, 0.421917`,
0.677286`, -0.34936`, -0.16841`, -0.24775`, 0.813205`,
0.421242`, -0.15486`, 0.612315`, 0.953073`, 0.561099`};
``````

Now lets plot your time history

``````   ListLinePlot[data]
`````` This has a mean value which it is best to remove since it can dominate a spectrum. I remove the mean and do a Fourier analysis to get the spectrum and plot.

``````  data1 = data - Mean[data];
ft = Fourier[data1];
ListLinePlot[Abs[ft]]
`````` This is your spectrum. I have taken the absolute value because the spectrum has complex values. The horizontal axis is the frequency but I have not put on a frequency axis the numbers are point numbers. You will see it is symmetric. This is correct. For more details on Fourier analysis see here. Hope that helps.

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