Difference between revisions of "HW2-D Jeremiah Wise ECE301Fall2008mboutin" - Rhea

Revision as of 16:21, 12 September 2008

A system is time invariant if for any time shifted input signal the system produces a shifted output such that if an input $ x(t) $ produced an output $ y(t) $ then the input $ x(t + t_0) $ would produced the output $ y(t + t_0) $

Time Invariant Signal

$ S_1(t) = 5x(t) $

$ S_2(t) = t - t_0 $

$ x(t) -> S_1(t) -> S_2(t) -> 5x(t - t_0) $

$ x(t) -> S_2(t) -> S_1(t) -> 5x(t - t_0) $

This means that $ S_1(t) = 5x(t) $ is a time invariant signal.

Time Variant Signal

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

$ S_2(t) = t - t_0 $

$ x(t) -> S_1(t) -> S_2(t) -> 5x(1 - t + t_0) $

$ x(t) -> S_2(t) -> S_1(t) -> 5x(1 - t - t_0) $

This means that $ S_1(t) = 5t $ is a time invariant signal.