engineering recuitment MAHATRANSCO AE Electrical Mock Test Signals and Systems Z Transform Unilateral Z Transform
The unilateral z transform of \({\rm{x}}\left[ {\rm{n}} \right] = {\left( {\frac{1}{2}} \right)^{{\rm{n}} + 1}}{\rm{u}}\left[ {{\rm{n}} + 5} \right]\) is
1
\(\frac{{{{\rm{z}}^{ - 5}}}}{{1 - \frac{1}{2}{{\rm{z}}^{ - 1}}}};\ \rm ROC:\left| {\rm{z}} \right| > \frac{1}{2}\)
2
\(\frac{1}{{1 - \frac{1}{2}{{\rm{z}}^{ - 1}}}};\ \rm ROC:\left| {\rm{z}} \right| > \frac{1}{2}\)
3
\(\frac{1}{2} \cdot \frac{1}{{1 - \frac{1}{2}{{\rm{z}}^{ - 1}}}};\ \rm ROC:\left| {\rm{z}} \right| > \frac{1}{2}\)
4
\(\frac{1}{2}\frac{{{{\rm{z}}^{ - 5}}}}{{1 - \frac{1}{2}{{\rm{z}}^{ - 1}}}};\ \rm ROC:\left| {\rm{z}} \right| < \frac{1}{2}\)
5
None of the above