( 25 pts) A causal LTI system T with input x[n] and output y[n] is described by the difference equation,
y[n]=x[n]-4x[n-2]+(3)/(4)y[n-1]-(1)/(8)y[n-2]
As usual, the impulse response of T is denoted as h[n] and the transfer function is denoted as H(z).
(a) (7 pts) Find H(z), identify its poles and specify the Region of Convergence (ROC). Justify your
choice of the ROC.
(b) ( 3 pts ) Is T a stable system? Why, or why not?
(c) (5 pts) Draw the Direct Form II Block Diagram for the system T. What distinguishes a Direct
Form II block diagram from a Direct Form I block diagram?
(d) (5 pts) Find the output of T if the input signal is x[n]=1+2+2^(n+1). Show your work.
(e) (5 pts) Find the first three non-zero sample values of h[n]. Show your work.
