Discrete step function

Definition

1(k)={1for k≥00otherwise1(k) = \begin{cases} 1 \quad \text{for } k \geq 0 \\ 0 \quad \text{otherwise} \end{cases}

Relationship between discrete delta, step, delta response, step response

δ(k)=1(k)−1(k−1)1(k)=∑j=0∞δ(k−j)h(k,i)=a(k,i)−a(k,i+1)a(k,i)=∑j=0∞h(k,i+j)\begin{eqnarray} \delta(k) = 1(k) - 1(k-1) \\ 1(k) = \sum_{j=0}^\infty \delta(k-j) \\ h(k,i) = a(k,i) - a(k,i+1) \\ a(k,i) = \sum_{j=0}^\infty h(k,i+j) \end{eqnarray}