What is the partial fraction expansion of X(z)= (1+z-1)/(1-z-1+0.5z-2 )?
A. (z(0.5-1.5j))/(z-0.5-0.5j) – (z(0.5+1.5j))/(z-0.5+0.5j)
B. (z(0.5-1.5j))/(z-0.5-0.5j) + (z(0.5+1.5j))/(z-0.5+0.5j)
C. (z(0.5+1.5j))/(z-0.5-0.5j) – (z(0.5-1.5j))/(z-0.5+0.5j)
D. (z(0.5+1.5j))/(z-0.5-0.5j) + (z(0.5-1.5j))/(z-0.5+0.5j)
Answer:A
What is the partial fraction expansion of X(z)= (1+z-1)/(1-z-1+0.5z-2 )?
A. (z(0.5-1.5j))/(z-0.5-0.5j) – (z(0.5+1.5j))/(z-0.5+0.5j) B. (z(0.5-1.5j))/(z-0.5-0.5j) + (z(0.5+1.5j))/(z-0.5+0.5j) C. (z(0.5+1.5j))/(z-0.5-0.5j) – (z(0.5-1.5j))/(z-0.5+0.5j) D. (z(0.5+1.5j))/(z-0.5-0.5j) + (z(0.5-1.5j))/(z-0.5+0.5j)
Explanation: To eliminate the negative powers of z, we multiply both numerator and denominator by z2. Thus,