How to extract envelope for piecewise defined function?

I have a plot generated from an ugly and complex set of piece-wise functions. I’m looking to extract the envelope function from this data set. I’ve tried a lot of suggestions in other threads, but none seem to contain information about dealing with piece-wise functions. I’ve tried using a Fourier series, but that didn’t seem to give me what I was looking for. The plot is located belowenter image description here

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