``Classic'' Amplitude Modulation

``Classic'' amplitude modulation (AM) is the more general of the two techniques.

In AM, the modulating signal includes a constant, a DC component, in the modulating term,

$$x(t) = [A_0 + \cos(2\pi f_\Delta t)]\cos(2\pi f_c t).$$

Multiplying out the above equation yields

$$x(t) = A_0\cos(2\pi f_c t) + \cos(2\pi f_\Delta t)\cos(2\pi f_c t).$$

The first term in the result above shows that the carrier frequency is actually present in the resulting spectrum.

The second term can be expanded in the same way as was done for ring modulation, using the inverse Euler formula (left as an exercise).