You asked something very complicated my friend...
As far as I know, you can do this normalization by application, depending on the music player or video player you are using, there's an configuration for activating normalization.
Now, if you desire to use normalization on the whole system, as a global solution... you'll have to get very technical, there's a way, and it should work, it is called LADSPA
or Linux Audio Developer's Simple Plugin API.
- Install requirements:
sudo eopkg it ladspa swh-plugins
- Now open a terminal and run
pacmd
- Type:
load-module module-ladspa-sink sink_name=compressor plugin=sc4m_1916 label=sc4m control=1,1.5,401,-30,20,5,12 set-default-sink compressor
Test, see if it works. Source, it not permanent, after rebooting it will reset to normal, so if it worked you'll have to repeat the steps again... or create an script and set it to autostart with the system.