Consider the difference equation of Eq. (3.66). (a) Show that with nonzero initial...

Consider the difference equation of Eq. (3.66).

(a) Show that with nonzero initial conditions the unilateral z-transform of the output of the difference equation is

(b) Use the result of (a) to show that the output has the form

y[n] = yZIR[n] + yZICR[n] where yZIR[n]

is the output when the input is zero for all n and yZICR[n] is the output when the initial conditions are all zero.

(c) Show that when the initial conditions are all zero, the result reduces to the result that is obtained with the bilateral z-transform.