engineering recuitment GATE ECE 2023-24 Test Series Signals and Systems Z Transform Inverse Z Transform
The X(z) has poles at \(z = \frac{1}{2}\) and z = -1. If x[1] = 1, x[-1] = 1, and the ROC includes the point \(z = \frac{3}{4}\), the time signal x[n] is
1
\(\frac{1}{{{2^{n - 1}}}}u\left[ n \right] - {\left( { - 1} \right)^n}u\left[ { - n - 1} \right]\)
2
\(\frac{1}{{{2^n}}}u\left[ n \right] - {\left( { - 1} \right)^n}u\left[ { - n - 1} \right]\)
3
\(\frac{1}{{{2^{n - 1}}}}u\left[ n \right] + u\left[ { - n + 1} \right]\)
4
\(\frac{1}{{{2^n}}}u\left[ n \right] + u\left[ { - n + 1} \right]\)