The Carrier signal is a sinusoid with a fixed Frequency at least twice as high as the highest frequency occuring in the spectrum of the incoming signal
Sorry Holger, but that's wrong. This is only valid if you try to digitilize an analog signal. What you're thinking of is the Nyquist Theorem, but thats another business..
@ FIXME: is this formula correct, shouldn't theh transformation in frequency domain depend on frequency instead of time? As soon this is cleared we can transform the image entirely into TeX...
, you're right.
it simply describes the carrier frequency 2*Pi*fc and around the carrier frequency two additional frequencies in the distance of the modulating omega_m: 2*Pi(fc + fm) and 2*Pi*(fc - fm).