# Digital Modulation

Learn how information is communicated in digital systems from point A to point B.

## We'll cover the following

A digital source produces a sequence of bits in the form of $0$s and $1$s. The question is how to send these bits from point A to point B. For this purpose, an **electromagnetic wave** acts as a carrier of information.

Remember that the signal produced by an unmodulated electromagnetic wave is a sinusoid given as:

$x(t) = A \cos \left(2\pi ft + \theta\right)$

There are three *tunable* parameters, which are listed below:

- Amplitude $A$
- Frequency $f$
- Phase $\theta$

Information can be conveyed by altering any of these parameters.

Let’s explore them below.

## Amplitude shift keying

The process starts with converting the bits of $0$s and $1$s into voltage levels known as *symbols*, for example:

$\begin{align*} 0 \quad &\longrightarrow \quad 1 \\ 1 \quad &\longrightarrow \quad 2 \end{align*}$

This is called * binary modulation*. To keep the contents simple, we will focus on binary modulations only. Otherwise, multiple bits can also be assigned to a symbol. For instance, a

*can represent the sets of $2$ bits as:*

**quaternary modulation**$\begin{align*} 00 \quad &\longrightarrow \quad -3 \\ 01 \quad &\longrightarrow \quad -1 \\ 10 \quad &\longrightarrow \quad +1 \\ 11 \quad &\longrightarrow \quad +3 \end{align*}$

The *serial-to-parallel converter* we saw in the OFDM block diagram represents this aggregation of bits ($2$ in this case) for subsequent mapping to a signal level.

Let’s investigate how a sinusoidal wave can be modulated in amplitude.

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