Let T be an LTI, relaxed, and BIBO stable system with input x(n) and output y(n) show that:
(a) If x(n) is periodic with period N [i.e., x(n) = x(n + N) for all n ≥0], the output y(n) tends to a periodic signal with the same period.
(b) If x(n) is bounded and tends to a constant, the output will also tend to a constant.
(c) If x(n) is an energy signal, the output y(n) will also be an energy signal.