Consider a causal LTI systemS with input x[n] and a system function specified as H(z) =

Chapter 10, Problem 10.38

(choose chapter or problem)

Consider a causal LTI systemS with input x[n] and a system function specified as H(z) = H1 (z)H2(z), where and A block diagram corresponding to H(z) may be obtained as a cascade connection of a block diagram for H 1 (z) followed by a block diagram for H2(z). The result is shown in Figure PI 0.38, in which we have also labeled the intermediate signals e1 [n], e2[n], !1 [n], and f2[n]. (a) How is e1 [n] related to / 1 [n]? (b) How is e2[n] related to f2[n]? y[n] Figure P1 0.38 (c) Using your answers to the previous two parts as a guide, construct a directform block diagram for S that contains only two delay elements. (d) Draw a cascade-form block diagram representation for S based on the observation that H(z) = 4 ( 1 + lz- 1 )(1- 2z-I) 1 + ~ z- 1 1 - ~ z- 1 (e) Draw a parallel-form block diagram representation for S based on the observation that 5/3 H(z) = 4 + ----=--- 1 + lz-I 2 14/3 1- lz-I.