I am trying to expand an explicit piecewise equation as a Fourier series formulation using Wolfram Mathematica software.
An example of these expansions is depicted in this paper (Article Quantitative Analysis of Contribution of Airgap Field Harmon...
).The two piecewise multi-parameter equations (eq. 12 & 13) are transformed into two Fourier series equations (eq. 14 & 15).
What is the best way to go about performing this expansion and how?
You would perform an FFT on the time series and the value for the Fourier coefficients would be produced. You'll get a quite a few, so, truncating the coefficient series will be in order. From the truncated set of coefficients, you could could then build an analytic model.
If you want analytic expansions, you would need to produce the model first, then expand or fit that model to the time series, whether it were in time or frequency, regardless.
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