If I plot the spectrum of a short modem signal, what should I expect > to see?
authoritative answer: "It depends."
On a WHOLE lot of things you didn't bother to mention.
2-wire vs 4-wire. (i.e. dialup vs. lease-line.)
FDX or HDX (two modems talking *simultaneously* to each other, or *one* talking while the other only 'listens').
Modulation methodology (e.g. FSK, QAM, PEP, PFSK, etc.)
Encoding.
Modulation 'protocol' (e.g. Bell 202T, Bell 208A, V.42bis, V90, etc.)
Data rate.
And the *actual*data* being transmitted at the time.