Time invariance is where the output is not effected by time. As the book puts it the behavior and characteristics of the system are fixed over time.


Time Invariant Problem

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

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

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

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

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

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

Since they are equal it is time invariant.


Time Variant Problem

(Time variant problem was taken from the in class "exercise" section I posted)

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

$ 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) $

Since they are not equal it is time variant.

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang