In order to define a contextual action for spectrum layers, you need to put your Python script in your Python directory under a directory called Contextual_Spectrum_Analysis_Spectrum_Layer.
Go to Tools->Options->Environment->Python Scripts (or Tools->Options->Python->Scripts in INTViewer 5.2) and click "Refresh from Disk". Your script should be listed automatically.
You will now be able to execute this script from the contextual menu of the spectrum layer:
This script will set the windowing, filtering, trend removal and smoothing of the spectrum, in addition to using Hilbert Trend Removal, Power Density Weights and Power Smoothing.
The script is attached to the bottom of this article.
The result after the script executes should look something like this: