(New page: == Time Invariance == === Background === A time invariant system refers to a system where the time has no affect on the amplitude of the function. To put it another way, time is never ...) |
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== Time Invariance == | == Time Invariance == | ||
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=== Background === | === Background === | ||
| − | A time invariant system refers to a system where the time has no affect on the amplitude of the function. To put it another way, time is never multiplied | + | A time invariant system refers to a system where the time has no affect on the amplitude of the function. To put it another way, time is never multiplied or taken to any power, affecting the amplitude |
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=== Example of Time Invariant function === | === Example of Time Invariant function === | ||
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| + | <math>y(t)=2x(t)cos(t)+1</math> because replace t with <math>x_1=x(t-k)</math> , | ||
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| + | <math>y_1(t-k)=2x_1cos(t)+1=2x(t-k)cos(t-k)+1</math> | ||
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| + | Now shifted again | ||
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| + | <math>y_2=y(t-k)=x2x(t-k)cos(t-k)+1=y_1(t)</math> | ||
=== Example of Time Variant function === | === Example of Time Variant function === | ||
Revision as of 15:33, 11 September 2008
Contents
Time Invariance
Background
A time invariant system refers to a system where the time has no affect on the amplitude of the function. To put it another way, time is never multiplied or taken to any power, affecting the amplitude
Example of Time Invariant function
$ y(t)=2x(t)cos(t)+1 $ because replace t with $ x_1=x(t-k) $ ,
$ y_1(t-k)=2x_1cos(t)+1=2x(t-k)cos(t-k)+1 $
Now shifted again
$ y_2=y(t-k)=x2x(t-k)cos(t-k)+1=y_1(t) $
