You might add the random sine waves in the time sequence.

Let say your spectrum has 1000 points array.

divide spectrum in to 10 bins, each bin will have 100 points.

now calculate mean of each bin, use it for your processing.

For discontinues of spectrum : put the magnitude threshold and discard.

https://blog.endaq.com/calculate-power-spectral-density-using-the-endaq-open-source-python-library