Background: Amplitude modulation (AM) is a common technique used to modulate communications signals. AM works by altering the amplitude of the output signal with relation to the data being sent. Amplitude modulation was chosen to be used for radio transmission because of it's relatively cheap and simple design.
Example of Double-Sided Amplitude Modulation:
Carrier: c(t) = C(sin(w_c*t + B_c)) , where C and B_c are constants for amplitude and phase. w_c/2pi is the carrier frequency (e.g. this is the frequency that you would tune to on your AM radio).
Data: X(t) = M(cos(w_m*t + B)), where M is largest magnitude of data signal
Modulation: y(t) = c(t)[A + x(t)], where A is a constant s.t. A>=M
So, y(t) = sin(w_c*t)[A + M(cos(w_m*t + B))]
