I used python to convert the time-domain signal below into a frequency spectrum so that I can analyze the harmonics. To do this I used Python libraries, specifically numpy and called fft to get the spectrum. I now want to validate my results. I have x, y coordinates in Excel and the plot below. To validate, I know that I could try to compute the Fourier series myself. The problem that I'm having is that I can't actually figure out how to begin. I don't know the equation of the waveform below so I can't use the definition of the Fourier transform. Any ideas on how to do this manual validation (or any other suggestions on how to actually confirm whether my fft is correct) are extremely helpful.
Here's a plot of the time domain signal.
Here's a plot of the frequency domain spectrum.
