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==Time Invariance== | ==Time Invariance== | ||
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| + | A system is considered time-invariant if the following two orders of operations performed on a function <math>x(t)\!<\math> yield the same result: | ||
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| + | 1. The function is put through the system, and then, the function is shifted in time. | ||
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| + | 2. The function undergoes a time shift, and then, the function goes through the system. | ||
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| + | An example of a time invariant system is as follows: | ||
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| + | <math>y(t) = 2x(t)\!<\math> | ||
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| + | The proof for this is rather simple. Suppose <math>x(t) = t - 12\!<\math>. After going through the system, we are left with <math>2t - 24\!<\math>. After a time shift of, let's say <math>5\!<\math>, we are left with <math>2(t - 5) - 24\!<\math>, which is the same as <math>2t - 34\!<\math>. | ||
Revision as of 13:48, 11 September 2008
Time Invariance
A system is considered time-invariant if the following two orders of operations performed on a function $ x(t)\!<\math> yield the same result: 1. The function is put through the system, and then, the function is shifted in time. 2. The function undergoes a time shift, and then, the function goes through the system. An example of a time invariant system is as follows: <math>y(t) = 2x(t)\!<\math> The proof for this is rather simple. Suppose <math>x(t) = t - 12\!<\math>. After going through the system, we are left with <math>2t - 24\!<\math>. After a time shift of, let's say <math>5\!<\math>, we are left with <math>2(t - 5) - 24\!<\math>, which is the same as <math>2t - 34\!<\math>. $
