If your function is Gaussian (note that it is different from Gauss) or Lorentz, the w parameter is the FWHM. When fitting with the Gauss function, the FWHM is output to the report.Maybe I don't understand what you mean but to answer your question, I use a spline because the corresponding x values of the half maximum values of y on the left and right side of the maximum of the plot will be needed to calculate the fwhm and these indices are hardly present in real world data without interpolation.
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