The diagram in Fig. 1 depicts a cascade connection of two linear time-invariant systems, w...

The diagram in Fig. 1 depicts a cascade connection of two linear time-invariant systems, where the first system is a 3-point moving averager and the second system is a first difference.

Figure 1

(a) If the input is of the form x[n] = 10 + x1[n], the output, y[n], of the overall system will be of the form y[n] = y1[n], where y1[n] is the output due only to x1[n]. Explain why this is true.

(b) Determine the frequency-response function of the overall cascade system.

(c) Sketch the frequency-response (magnitude and phase) functions of the individual systems and the overall cascade system for

(d) Obtain a single-difference equation that relates y[n] to x[n] for the overall cascade system.