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== TIME INVARIANCE == | == TIME INVARIANCE == | ||
<pre> | <pre> | ||
| − | A system is defined as "time invariant" when its output is not an explicit function of time. | + | A system is defined as "time-invariant" when its output is not an explicit function of time. |
| − | To figure out whether a system is time invairant, we need to look for a value t outside of the | + | To figure out whether a system is time-invairant, we need to look for a value t outside of the |
normal x(t) or y(t). If it does not contain such a value t outside of the x(t), then it is time | normal x(t) or y(t). If it does not contain such a value t outside of the x(t), then it is time | ||
invariant. For instance, consider the following systems: | invariant. For instance, consider the following systems: | ||
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B.) h2(t) = 6t*x2(3t) + 5 | B.) h2(t) = 6t*x2(3t) + 5 | ||
| − | System A does not contain a "t" outside of the x1(3t). Therefore, we can call it time invariant. | + | System A does not contain a "t" outside of the x1(3t). Therefore, we can call it time-invariant. |
| − | However, system B does contain a "t" outside of the x2(3t). Thus, system B is not time invariant. | + | However, system B does contain a "t" outside of the x2(3t). Thus, system B is not time-invariant. |
</pre> | </pre> | ||
Revision as of 07:47, 11 September 2008
TIME INVARIANCE
A system is defined as "time-invariant" when its output is not an explicit function of time. To figure out whether a system is time-invairant, we need to look for a value t outside of the normal x(t) or y(t). If it does not contain such a value t outside of the x(t), then it is time invariant. For instance, consider the following systems: SYSTEMS: A.) h1(t) = 2x1(3t) + 5 B.) h2(t) = 6t*x2(3t) + 5 System A does not contain a "t" outside of the x1(3t). Therefore, we can call it time-invariant. However, system B does contain a "t" outside of the x2(3t). Thus, system B is not time-invariant.
