"The BBE is supposed to be a phase alignment device. The idea is that when a signal is amplified frequencies overlap and you get distortion. The BBE process is supposed to remove this distortion improving clarity and timbre. It is not a compressor, limiter, expander or harmonic generator. The BBE like any other tool can be overused and much of an amplifiers distortion character can be lost with overuse."
and
"Sonic Stomp’s application of the BBE technology is just like its big brothers, using frequency-dependent time alignment with integrated amplitude compensation. What’s all that about? Simply put, it helps a speaker more faithfully reproduce the signal so more of the nuance and detail is revealed."
I read something about how it delays lower frequencies at like 2.5ms so that they hit your ears the same time as the higher frequencies.
I'm going to create an impulse response of the pedal today and see what happens. Thanks for your info, @kylotan .