Answer to Question #200594 in Electrical Engineering for Teng

Question #200594

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

(a) β„Ž(𝑛)=𝛿(𝑛)βˆ’π›Ώ(π‘›βˆ’2)

(b) β„Ž(𝑛)=𝑛𝑒(𝑛)


1
Expert's answer
2021-05-31T06:18:36-0400

"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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