When I was editing a podcast about 2 days ago (one of the ones that I started for Mr. Lalvani last year ;vp ) I found out about, as the title of this post is named; taking out background sounds while keeping the main background air sound.
As you can see in this image the part that is selected is where a loud breath that I want to take out. but notice I didn't select the very bottom. That's because the bottom part is the regular low pitch background sound, and if there wasn't that breathing sound part you would see that there wouldn't be any purple above the low pitch.
Now you see in this image that the breathing part is gone, yet the tiny red line on the bottom is still there. I want to make sure it's there, that way it matches up with the other silences without breaths, if I take it away, it sounds like totaly quiet, so that one might think the recording is over.
I'm sorry, but I can't get a pic of Adobe Audition (I just found out I can't take a screenshot on this computer), so you can try and imagine it.