Question #200594

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

(a) β(π)=πΏ(π)βπΏ(πβ2)

(b) β(π)=ππ’(π)

Expert's answer

"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)"

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