In the cascade system of Fig. P-9.6(a), it is known that the system function H(z) of the o...

In the cascade system of Fig. P-9.6(a), it is known that the system function H(z) of the overall system is the product of four terms

(a) Determine the poles and zeros of H(z) and plot them in the complex z-plane.

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(b) It is possible to determine two system functions H1(z) and H2(z) so that (1) the overall cascade system has the given system function H(z), and (2) the output of the first system is y1[n] = x[n] − x[n − 4], Find H1(z) and H2(z).

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(c) Determine the difference equation that relates y[n] to y1[n] for your answer in (b).