Continuous vs discrete signals

A continuous signal is a quantity that varies over continuous time. That is, the smallest measurement of time is infinitesimal.¹ A very simple example is $f(t) = \sin(t)$ where $t∈\mathbb{R}$.

A discrete signal is where the time values are discrete. For example, $f(t) = t^2$ where $t∈\mathbb{N}$. This would lead to $t, f(t)$ pairs: $(0,0), (1,1), (2, 4)...$. That is, the x-axis values are discrete.

You can convert a continuous signal to a discrete signal by picking a set of discrete numbers. This is sampling. See that page for an example.

In the world of audio:

• Analog signals, such as recording a singer, are continuous
• Digital signals, i.e. a stream of bits from an analog-to-digital converter, are discrete