# 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

 $m$ = 1
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.