(New page: == Time Invariance == A system is called time invariant if shifting it's input signal in time results in the same time shift propagated to its output. == Example of a Time Invariant Syste...) |
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== Example of a Time Invariant System == | == Example of a Time Invariant System == | ||
| − | Given the system <math>y(t) = 10x(t)</math> | + | Given the system <math>y(t) = 10x(t)</math>: |
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== Example of a Time Variant System == | == Example of a Time Variant System == | ||
| + | Given the system <math>y(t) = 6x(4t + 2)</math>: | ||
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| + | First, apply the time delay to the input <math>x(t)</math>: <math>w_1(t) = x(t-t_0)</math> | ||
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| + | Then feed <math>w(t)</math> into the system: <math>z_1(t) = 6x(4t - t_0 + 2)</math> | ||
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| + | Now, try using the system first: <math>w_2(t)=6x(4t + 2)</math> | ||
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| + | Applying the time delay: <math>z_2(t) = 6x(4t - 4t_0 + 2)</math> | ||
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| + | Since <math>z_1(t) \ne z_2(t)</math> the system is <b>NOT</b> Time Invariant. | ||
Latest revision as of 16:59, 11 September 2008
Time Invariance
A system is called time invariant if shifting it's input signal in time results in the same time shift propagated to its output.
Example of a Time Invariant System
Given the system $ y(t) = 10x(t) $:
First, apply the time delay to the input $ x(t) $: $ w_1(t) = x(t-t_0) $
Then feed $ w(t) $ into the system: $ z_1(t) = 10x(t-t_0) $
Now, try using the system first: $ w_2(t)=10x(t) $
Applying the time delay: $ z_2(t) = 10x(t-t_0) $
Since $ z_1(t) = z_2(t) $ the system is Time Invariant.
Example of a Time Variant System
Given the system $ y(t) = 6x(4t + 2) $:
First, apply the time delay to the input $ x(t) $: $ w_1(t) = x(t-t_0) $
Then feed $ w(t) $ into the system: $ z_1(t) = 6x(4t - t_0 + 2) $
Now, try using the system first: $ w_2(t)=6x(4t + 2) $
Applying the time delay: $ z_2(t) = 6x(4t - 4t_0 + 2) $
Since $ z_1(t) \ne z_2(t) $ the system is NOT Time Invariant.
