Had the frequency sweep modulation been linear, then I might suspect an other-than-natural source. But -- the freq sweep is nonlinear...
I just had a really cool thought, worthy (IMHO) of inclusion in a science-fiction story.
What if FRBs are caused by the lighting-off of a relativistic-drive spaceship somewhere far away? Perhaps with it's "exhaust" (or antenna, or plasma beam) aimed directly at us.
Kind of the galactic equivalent of the sound of a hot rod peeling out half a mile away.
FTL burnout...