# Amplitude Modulation

This is an example where mathematics is used in communication systems.

## What is Amplitude Modulation?

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:\[ F(t) = (1 + f(t)) \cos wt \]

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 \( f(t) = m \cos(s t) \). Hence \( F(t) \) becomes

\[ F(t) = (1 + m \cos(s t)) \cos(wt) \]

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.

## Interactive Tutorial on Amplitude Modulation

1 - click the button above "Plot Signal" to start.

2 - Set parameter m to zero, there is no modulation. Explain the graph obtained.

3 - Set parameter m to 1. Explain the graph obtained.

4 - Set parameter m to values larger than 1. Explain the graph obtained.