Continuous-time signal

Continuous-time signals are signals where time (the independent variable) ranges over the set of real numbers. They can sometimes map from:

$$x:\mathbb{R}\to \mathbb{R}$$ $$x:\mathbb{R}\to \mathbb{C}$$

where $\mathbb{C}$ has real and imaginary parts that are functions of time. A 2D map (like a topographical map):

$$x:{\mathbb{R}}^2\to \mathbb{R}$$

And a 3D signal (like video):

$$x:{\mathbb{R}}^2\times \mathbb{R}\to \mathbb{R}$$

To construct a CT signal from a DT signal, we can interpolate between points. One method is a zero-order hold, where we essentially hold the value until the next sampling time, then change:

$$x_{zoh}(t)=x[n];n{T}_s\le t<(n+1)T_s$$