engineering recuitment GATE ECE 2023-24 Test Series Signals and Systems Z Transform Properties of Z Transform
Let x1[n], x2[n] and x3[n] be three discrete time signals and X1(z), X2(z) and X3(z) be their z-transforms given as:
\({X_1}\left( z \right) = \frac{{{z^2}}}{{\left( {z - 1} \right)\left( {z - 0.5} \right)}}\;\),
\({X_2}\left( z \right) = \frac{z}{{\left( {z - 1} \right)\left( {z - 0.5} \right)}}\)
\({X_3}\left( z \right) = \frac{1}{{\left( {z - 1} \right)\left( {z - 0.5} \right)}}\)
Then x1[n], x2[n] and x3[n] are related as:1
x1[n - 2] = x2[n - 1] = x3[n]
2
x1[n + 2] = x2[n + 1] = x3[n]
3
x1[n ] = x2[n - 1] = x3[n - 2]
4
x1[n + 1] = x2[n - 1] = x3[n]