Hi Jan,
Goldwave is the audio editing software and VideoMeld is the video editing software.
Goldwave is one of the most comprehensive audio editing software I've encountered. If you're curious about it, download the trial version and give it a test run. It's fully operational.
As mentioned in my original post, the function that I most often use is the Noise Reduction Filter.

What I do is to record a snippet of an audio file that contains the background noise of my studio (computer hum). When in Goldwave, I then copy the a section of that file to the clipboard. By selecting the the "Use clipboard" option on the left (in the below image), Goldwave then analyses the audio and subtracts those frequencies from my recordings of vocals. It's amazing how much extra clarity doing this adds to my vocals.

Regards,
Noel