When implemented with infinite-precision arithmetic, the flow graphs in Figure P6.59 hav...

When implemented with infinite-precision arithmetic, the flow graphs in Figure P6.59 have the same system function.

(a) Show that the two systems have the same overall system function from input x[n] to output y[n].

(b) Assume that the preceding systems are implemented with two’s complement fixed point arithmetic and that products are rounded before additions are performed. Draw signal flow graphs that insert round-off noise sources at appropriate locations in the signal flow graphs of Figure P6.59.

(c) Circle the nodes in your figure from part (b) where overflow can occur.

(d) Determine the maximum size of the input samples such that overflow cannot occur in either of the two systems.

(e) Assume that |a| < 1. Determine the total noise power at the output of each system, and determine the maximum value of |a| such that Network 1 has lower output noise power than Network 2.