Suppose that three systems are connected in cascade; i.e., the output of  is the input to...

Suppose that three systems are connected in cascade; i.e., the output of  is the input to  and the output of  is the input to . The three systems are specified as follows:

where the output of  is yi,[n] and its input is xj[n]

(a) Determine the equivalent system that is a single operation from the input x[n] (into ) to the output y[n], which is the output of . Thus, x[n] is x1[n] and y[n] is y3[n].

(b) Use the frequency response to write one difference equation that defines the overall system in terms of x[n] and y[n] only.