GATE 2015 EE - SET 2 - Question 35

Solution :

x[Z]  = 2Z + 4 - \frac{4}{Z} + \frac{3}{Z^{2}}

y(x) is the first diiferences of x[x]
y(n)= x(n) - x(n-1)

Y[Z] = X[Z][1-Z^{-1}]

Y[Z] = X[Z][1-\frac{1}{Z}]

Y[Z]= (1-\frac{1}{Z})(2Z+4-\frac{4}{Z}+\frac{3}{Z^{2}})

Y[Z]= (2Z+2-\frac{8}{Z}+\frac{7}{Z^{2}}- \frac{3}{Z^{3}})