The z-transform X(z) of a real and right-sided sequence x[n] has exactly two poles and one of them is at z = e^i 2 and there are two zeros at the origin. If x(1) = 1, which one of the following is TRUE?

X( z ) = 2z^2z^2 + 1,ROCis| z | > 1

This question belongs to Electronics And Communications Engineering Signal Processing

Signal Processing

The z-transform X(z) of a real and right-sided sequence x[n] has exactly two poles and one of them is at $$z = {e^{\frac{{i\pi }}{2}}}$$ and there are two zeros at the origin. If x(1) = 1, which one of the following is TRUE?

A) $$X\left( z \right) = \frac{{2{z^2}}}{{{{\left( {z - 1} \right)}^2} + 2}},\,{\text{ROC}}\,{\text{is}}\,\frac{1}{2} < \left| z \right| < 1$$ B) $$X\left( z \right) = \frac{{2{z^2}}}{{{z^2} + 1}},\,{\text{ROC}}\,{\text{is}}\,\left| z \right| > \frac{1}{2}$$ C) $$X\left( z \right) = \frac{{2{z^2}}}{{{{\left( {z - 1} \right)}^2} + 2}},\,{\text{ROC}}\,{\text{is}}\,\left| z \right| > 1$$ D) $$X\left( z \right) = \frac{{2{z^2}}}{{{z^2} + 1}},\,{\text{ROC}}\,{\text{is}}\,\left| z \right| > 1$$

Answer & Solution

Correct Answer: Option D

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The z-transform X(z) of a real and right-sided sequence x n...

The z-transform X(z) of a real and right-sided sequence x[n] has exactly two poles and one of them is at $$z = {e^{\frac{{i\pi }}{2}}}$$ and there are two zeros at the origin. If x(1) = 1, which one of the following is TRUE?

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