The carrier signal is generally a high-frequency sine wave. There are three parameters of a sine wave that can be varied: amplitude, frequency, and phase. Any of these can be modulated, or varied, to transmit information. A sine wave can be mathematically described by a sine or cosine function with amplitude Ac, frequency fc, and phase φ.
Figure 2. Carrier Wave
The carrier signal is modulated by varying its amplitude in proportion to the message, or baseband, signal. The message signal can be represented by
and the carrier signal can be represented by
To make the equations simpler, assume that there is no phase difference between the carrier signal and the message signal and thus φ = 0.
The modulated signal can be represented by multiplying the carrier signal and the summation of 1 and the message signal, as shown below.
With some basic trigonometric manipulation, the above waveform can be written as