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Given the finite lengt h input x[n] and the corresponding finite length output y[n] of an LTI system as shown below. The impulse response h[n] of the system is
Correct Option: C
x[n] = {1, – 1}, N = 2
y[n] = {1, 0, 0, 0, – 1}, N = 5
If P is t he number of elements in impulse response h[n], then,
⇒ N = M + P – 1
⇒ 5 = 2 + P – 1
⇒ P = 4
Let h[n] = {x1, x2, x3, x4}
then, y[n] = {x1, (x2 – x2), (x3 – x2), (x4 – x3), – x1}
Comparing with y[n] = {1, 0, 0, 0, – 1}
↑
We get x1 = 1, x2 = x1 = 1, x3 = x4 =1, x4 = x3 = 1
then, h[n] = {1, 1, 1, 1}
