Problem 4. Consider a digital filter with the transfer function H(z)=\frac{Y(z)}{X(z)}=\frac{1}{0.5+z^{-1}}, \quad|z|>0.5 If we set the input as a[n] = u[n]: a. Find the analytic expression for y[n] directly using

a PFE. (Hint: First compute X(z) = Z{r[n]}) b. Express y[n] in the form of a difference equation.