Example: Double-sideband AM
A carrier wave is modeled as a sine wave:
in which the frequency in Hz is given by:
The constants and represent the carrier amplitude and initial phase, and are introduced for generality. For simplicity, their respective values can be set to 1 and 0.
Let m(t) represent an arbitrary waveform that is the message to be transmitted, i.e., a simple audio tone of form:
where constant M represent the largest magnitude, and the frequency is:
It is assumed that and that
Amplitude modulation is formed by the product:
represents the carrier amplitude, which is a constant that demonstrates the modulation index. The values A=1 and M=0.5 produce y (t), depicted by the top graph (labelled "50% Modulation") in Figure 4. Using trigonometric identities, y(t) can be written in the form
Therefore, the modulated signal has three components: a carrier wave and two sinusoidal waves (known as sidebands), whose frequencies are slightly above and below
Read more about this topic: Amplitude Modulation