engineering recuitment GATE ECE 2023-24 Test Series Signals and Systems Z Transform Inverse Z Transform
Find the inverse Z-transform of \(X\left( z \right) = \frac{1}{{1 - \frac{1}{4}{z^{ - 2}}}},\;\left| z \right| < \frac{1}{4}\)
1
\(\mathop \sum \limits_{K = 0}^\infty {2^K}\delta \left( {n + 2K} \right)\)
2
- \( \mathop \sum \limits_{K = 0}^\infty {2^{2K}}\delta \left( {n + 2K + 1} \right)\)
3
- \( \mathop \sum \limits_{K = 0}^\infty {2^{2K + 2}}\delta \left( {n + 2K + 2} \right)\)
4
\(\mathop \sum \limits_{K = 0}^\infty {2^{K - 2}}\delta \left( {n + K} \right)\)