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Question

# Consider a discrete time signal x[n] and its z-transform, X(z) given as X(z)=z2+5zz2âˆ’2zâˆ’3 If ROC of X(z) is |z|<1, then signal x[n] would be

A
[2(3)n(1)n]u[n]
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B
[2(3)n+(1)n]u[n1]
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C
2(3)nu[n1](1)nu[n]
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D
[2(3)n+1]+u[n]
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Solution

## The correct option is B [−2(3)n+(−1)n]u[−n−1] X(z)=z2+5zz2−2z−3=z(z+5)(z−3)(z+1) X(z)z=z+5(z−3)(z+1)=2z−3−1z+1 Thus, X(z)=2zz−3−zz+1 ROC : |z| < 1, which is not exterior of circle outside the outermost pole = 3 So, x[n] is anti-causal given as, x[n]=[−2(3)n+(−1)n]u[−n−1]

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