This is simple example where mathematics is used in communication systems.
F(t) = (1 + f(t)) * cos wt
Amplitude modulation is a technique used to transmit electric signals, containing information, using radio waves. Let f(t) be the electric signal to transmit (we represent a signal that carries information by a mathematical function f(t)) and cos wt the carrier signal (the signal that will carry signal f(t)). Let the amplitude of cos wt change in terms of f(t) as follows:
This is called amplitude modulation since the amplitude of the carrier cos wt changes in terms of f(t). In order to understand exactly what is meant by amplitude modulation, let the electric signal to transmit be a simple sinusoidal signal of the form f(t) = m cos st. Hence F(t) becomes
F(t) = (1 + m cos st) * cos wt
The applet below helps you explore the amplitude modulated signal F(t) when the amplitude m of the signal to transmit changes from 0 to larger positive values.
1 - click on the button above "click here to start" and MAXIMIZE the window obtained.
2 - Use the slider to set parameter m to zero, there is no modulation. Explain the graph obtained.
3 - Use the slider to set parameter m to 1. Explain the graph obtained.
4 - Use the slider to set parameter m to values larger than 1. Explain the graph obtained.