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Question

# Consider Two LTI system in cascade as shown below, y(n) is output . if h1(n)=3nu(n) and h2(n)=3δ(n)−9δ(n−1) if x(n) = sin(n) then

A
y(n)[δ(n)δ(n1)]=3sin(n)3sin(n1)
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B
y(n)=5sin(n2)+3sin(n)
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C
y(n)[δ(n)δ(n1)]=5sin(n/2)3sin(n1)
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D
y(n) = 3sin(n)
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Solution

## The correct option is A y(n)∗[δ(n)−δ(n−1)]=3sin(n)−3sin(n−1) (a,c) In the given question two LTI system are in cascade the overall impulse response will be h(n)=h2(n)∗h1(n) = [3δ(n)−9δ(n−1)]∗3nu(n) =3n+1u(n)−3n+1u(n−1) =3n+1u(n)−u(n−1) ==3n+1δ(n) h(n) = 3δ(n) Since input is sin(n) so output will be sin(n)*h(n) = 3δ(n) * sin(n) = 3 sin (n)

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