What is the definition of small/large signal bandwidth?
In communications, whether a signal is narrowband (has a small bandwidth) or wideband (has a large bandwidth) is relative to the channel's impulse response.

If the channel behaves as a flat filter (constant gain) over the signal's bandwidth, then the signal is narrowband. If the channel introduces significant distortion (that is, if different signal frequencies see different gain) then it is said that the signal is wideband.