Given f [n] = an u[n], find the z-transforms of the following:
(a) f[n – 3]u[n – 3]; verify your result by a power series expansion
(b) f [n + 3]u[n]; verify your result by a power series expansion
(c) Evaluate f[n] for n = 0 and n = 3, f [n – 3]u[n – 3] for n = 3, and f [n + 3]u[n] for n = 0 by converting each z-transform function into a power series.
(d) Are the values found in Part (c) consistent? Explain why or why not.
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