Question

Evaluate the step response of the LTI system represented by the following impulse response :

(a) ℎ(𝑛)=𝛿(𝑛)−𝛿(𝑛−2)

(b) ℎ(𝑛)=𝑛𝑢(𝑛)

Answer 1

$y(n)=h(n)*h(n) \implies (\delta (n)-\delta (n-2))*(\delta (n)-\delta (n-2))$

$\implies \delta (n)*\delta (n)-\delta (n-2)*\delta(n-\delta(n)* \delta(n-2))+\delta(n-2)*\delta(n-2)$

By using the above property

$\implies \delta(n)- \delta(n-2)- \delta(n-2)+\delta(n-4)$

$\implies \delta(n)- 2\delta(n-2)+\delta(n-4)$

$y(n)=\delta(n)-2 \delta(n-2)+\delta(n-4)$