(a) Consider the nonrecursive discrete-time LTI filter depicted in Figure P11.55(a). Thr...

(a) Consider the nonrecursive discrete-time LTI filter depicted in Figure P11.55(a). Through the use of feedback around this nonrecursive system, a recursive filter can be implemented. To do so, consider the configuration shown in Figure P11.55(b), in which 11(z) is the system function of the nonrecursive LTI system of Figure P11.55(a). Determine the overall system function of this feedback system, and find the difference equation relating the input to the output of the overall system.

In this problem, we have seen that the use of feedback provides us with alternative implementations of LTI systems specified by linear constant-coefficient difference equations. The implementation in part (a), consisting of feedback around a nonrecursive system, is particularly interesting, as some technologies are ide-ally suited to implementing tapped delay-line structures (i.e., systems consisting of chains of delays with taps at each delay whose outputs are weighted and then summed).