One message, four modulations. See the waveform and envelope, the spectrum line by line, and where the power goes. Push AM past μ = 1 to see overmodulation, and dial FM to β = 2.405 to watch the carrier vanish.
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Message m(t)
Modulated signal (carrier at 12× the message frequency)
Spectrum (amplitude of each frequency component; hollow = negative, i.e. 180° phase)
The carrier carries no information, yet at it takes of the power. Efficiency , and it is never better than , reached at .
Sidebands sit at with amplitude each, so the bandwidth is whatever is.
The dashed envelope is an exact copy of the message, which is why a simple diode-and-RC envelope detector works.