Questions

The input x(t) and the output Y(t) of a system are related by the equation

$ Y(t) = x(t - 1) - x(1 - t) $


Is the system Time Invariant? Justify your answer.

Answer

No.

$ S_1 = Y(t) = x(t - 1) - x(1 - t) $

$ S_2 = Y(t) = x(t - t_o) $

$ x(t) -> S1 -> S2 -> x(t - t_o - 1) - x(1 - t + t_o) $

$ x(t) -> S2 -> S1 -> x(t - t_o - 1) - x(1 - t - t_o) $

$ x(t - t_o - 1) - x(1 - t + t_o) =/= x(t - t_o - 1) - x(1 - t - t_o) $


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Followed her dream after having raised her family.

Ruth Enoch, PhD Mathematics