Impulse

In Discrete-Time land, an Impulse $\delta [n]$ is a Signal that is a discrete Kronecker Delta Function

$$\begin{array}{r}\delta [n]=\{\begin{array}{ll}1,& n=0\\ 0,& n\ne 0\end{array}\\ \\ \delta [n]=[1,\vec{0}]\end{array}$$

Note that for Convolutions, this unit impulse is like the Identity

$$x[n]\ast \delta [n]=x[n]$$

Similar to the Step Function, you can scale or shift the delta function. Furthermore, you can compose these scaled and shifted delta functions to create ANY given signal.

For example, $x[n]$ is a signal that goes: 1, 2, 3.

$$x[n]=1\cdot \delta [n]+2\cdot \delta [n-1]+3\cdot \delta [n-2]$$