If I plot the spectrum of a short modem signal, what should I expect > to see?
Depends on the modem.
It just looks like a lump in the frequency domain, but I'm not sure I > did it right.
If you make the bins small enough, you should see every individual carrier.
With a Bell 103 modem, there will be one carrier. With a modern 56k modem there will be dozens of them all across the band.
Scott "C'est un Nagra. C'est suisse, et tres, tres precis."