Suppose that three systems are connected in cascade. In other words, the output of S1 is t...

Suppose that three systems are connected in cascade. In other words, the output of S1 is the input to S2, and the output of S2 is the input to S3. The three systems are specified by their difference equations as follows:

Thus x1[n] = x[n], x2[n] = y1[n], x3[n] = y2[n], and y[n] = y3[n]. We wish to determine the equivalent system that is a single operation from the input x[n] (into S1) to the output y[n], which is the output of S3.

(a) Determine the impulse response hi[n] for each individual subsystem Si.

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(b) Determine the impulse response h[n] of the overall system, that is, find h[n] so that y[n] = x[n]* h[n].

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(c) Write one difference equation that defines the overall system in terms of x[n] and y[n] only.