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-$$\frac{8}{Z}+\frac{7}{Z^{2}}- \frac{3}{Z^{3}}$$)