Time Invariance Definition
A Time Invariant system is a system whose output does not depend explicitly on time.
Example of Time Invariant System
- $ y(t) = \tfrac{3}{5}x(t)\! $
- $ x(t)\! $ --> TIME DELAY --> $ y(t) = x(t - t_0)\! $ --> SYSTEM --> $ z(t) = \tfrac{3}{5}y(t) = \tfrac{3}{5}x(t - t_o) $
- $ x(t)\! $ --> SYSTEM --> $ y(t) = \tfrac{3}{5}x(t)\! $ --> TIME DELAY --> $ z(t) = y(t - t_0) = \tfrac{3}{5}x(t - t_o) $
Example of Time Variant System
- $ y(t) = tx(t)\! $
- $ x(t)\! $ --> TIME DELAY --> $ y(t) = x(t - t_0)\! $ --> SYSTEM --> $ z(t) = ty(t) = tx(t - t_o)\! $
- $ x(t)\! $ --> SYSTEM --> $ y(t) = tx(t)\! $ --> TIME DELAY --> $ z(t) = y(t - t_0) = (t - t_o)x(t - t_o)\! $
Going through the Time Delay then having the signal Transformed doesn't give us the same answer as having the signal transformed then going through the Time Delay.
- $ tx(t - t_o) \neq (t - t_o)x(t - t_o) $
