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[[Image:Timeproof_ECE301Fall2008mboutin.JPG]] | [[Image:Timeproof_ECE301Fall2008mboutin.JPG]] | ||
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where <math>y_1(t)\!</math> and <math>y_2(t)\!</math> are equal. | where <math>y_1(t)\!</math> and <math>y_2(t)\!</math> are equal. | ||
Revision as of 13:28, 11 September 2008
Time Invariance
A system is time-invariant if for any input $ x(t)\! $ and any $ t_0\! $ (where $ t_0\! $ is a real number) the response to the shifted input $ x(t-t_0)\! $ is $ y(t-t_0)\! $.
One can show a system is time invarient by proving
where $ y_1(t)\! $ and $ y_2(t)\! $ are equal.
Example of a Time Invariant System
Let $ y(t)=2x(t)+2\! $. The system is time invarient if for input $ x(t-t_0)\! $ the response is $ y(t-t_0)=2x(t-t_0)+2\! $.
