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Question

# The output sequence y[n] and the pulse response h[n] of a discrete system are given by, y[n]={1↑,1,2,−1,3} h[n]={1↑,2,3} The input sequence x[n] is

A
{1,1,1}
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B
{1,1,1}
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C
{1,1,1}
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D
{1,1,1}
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Solution

## The correct option is C {1↑,−1,1}H(z)=1+2z−1+3z−2 Y(z)=1+z−1+2z−2−z−3+3z−4 Y(z)X(z)=H(z) ⇒Y(z)H(z)=X(z) 1+2z−1+3z−2)1+z−1+2z−2−z−3+3z−4(1−z−1+z−1 1+2z−1+3z−2 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−z−1−z−2−z−3+3z−4 −z−1−2z−2−3z−3–––––––––––––––––––––– z−2+2z−3+3z−4 z−2+2z−3+3z−4 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ 0 –––––––––––––––––––– X(z)=1−z−1+z−2 x[n]={1↑,−1,1}

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