A linear time-invariant system is realized by the flow graph shown in Figure. (a) Write the difference

Question:

A linear time-invariant system is realized by the flow graph shown in Figure.

(a) Write the difference equation relating x[n] and y[n] for this flow graph.

(b) What is the system function of the system?

(c) In the realization of Figure, how many real multiplications and real additions are required to compute each sample of the output? (Assume that x[n] is real, and assume that multiplication by 1 does not count in the total.)

(d) The realization of Figure requires four storage registers (delay elements). Is it possible to reduce the number of storage registers by using a different structure? If so, draw the flow graph; if not, explain why the number of storage registers cannot be reduced.