2.1a.2 D-T Unit Step

Discrete-Time Unit Step

The discrete-time unit step can be defined as a signal $u:\mathbb{Z}\to \mathbb{Z}$, such that
$u[n]=\{\begin{array}{ll}0& \text{if }n<0\\ 1& \text{if }n\ge 0\end{array}.$
The unit step can be written in terms of a linear combination of shifted impulses as
$u[n]={\sum }_{k=0}^{}\delta [n-k]⟺u[n]={\sum }_{l=-\infty }^n\delta [l]⟸l=n-k.$