Problem

Consider the discrete-time system depicted in Figure P6.40-1. (a) Write the...

Consider the discrete-time system depicted in Figure P6.40-1.

(a) Write the set of difference equations represented by the flow graph of Figure P6.40-1.

(b) Determine the system function H₁(z) = Y₁(z)/X (z) of the system in Figure P6.40-1, and determine the magnitudes and angles of the poles of H₁(z) as a function of r for −1 < r < 1.

(c) Figure P6.40-2 shows a different flow graph obtained from the flow graph of Figure P6.40-1 by moving the delay elements to the opposite top branch. How is the system function H₂(z) = Y₂(z)/X (z) related to H₁(z)?