Partial fractions expansion inverse Z-transform, help

1. How do you solve inverse Z-transform?
2. How does the ROC help to find out inverse Z-transform?
3. How do you expand partial fractions?

How do you solve inverse Z-transform?

Long Division Method

X(z)=x(0)+x(1)Z−1+x(2)Z−2+......... The above sequence represents the series of inverse Z-transform of the given signal forn≥0 and the above system is causal. However for n<0 the series can be written as; x(z)=x(−1)Z1+x(−2)Z2+x(−3)Z3+.........

How does the ROC help to find out inverse Z-transform?

Inverse Z Transform

Region of Convergence (ROC) The ROC determines the region on the Z Plane where the Z Transform converges. The ROC depends solely on the 'r' value that is contained in 'z'.

How do you expand partial fractions?

A Simple Partial Fraction Expansion

To find A₁, multiply F(s) by s, and then set s=0. To find A₂, multiply F(s) by s+2 and set s=-2. The result can be simply checked by putting all of the expanded terms over a common denominator.