@Andy: Thanks for the overview. FFTs and Taylor series I am familiar with, at least from the hairy-knuckled engineer's side, and have been exposed to Volterra series because it is used in e.g. RF/microwave large-signal steady-state analysis (simulators), plus I have lecture notes from Ray Maas' seminar. That was long ago and I have mercifully forgotten most of it...
Oh yeah, Steve Maas from Applied Wave Research. I met him at an MTT in Phoenix, he's a nice guy. They used to make a Volterra simulator, but I think they gave that up to concentrate on harmonic balance, didn't they? I have been retired for a while so I've lost track.