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: Option D
This Question Belongs to Electronics And Communications Engineering >> Signal Processing
The Fourier transform of a real valued time signal has
A. Odd symmetry
B. Even symmetry
C. Conjugate symmetry
D. No symmetry
A. $$V$$
B. $${{{T_1} - {T_2}} \over T}V$$
C. $${V \over {\sqrt 2 }}$$
D. $${{{T_1}} \over {{T_2}}}V$$
A. $$T = \sqrt 2 {T_s}$$
B. T = 1.2Ts
C. Always
D. Never
A. $${{\alpha - \beta } \over {\alpha + \beta }}$$
B. $${{\alpha \beta } \over {\alpha + \beta }}$$
C. α
D. β
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