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A system is defined as "time-invariant" when its output is not an explicit function of time. In other | A system is defined as "time-invariant" when its output is not an explicit function of time. In other | ||
words, if one were to shift the input/output put along the time axis, it would not effect the general | words, if one were to shift the input/output put along the time axis, it would not effect the general | ||
| − | form of the function. One of the simplest ways to determine whether or not a system is time | + | form of the function. One of the simplest ways to determine whether or not a system is time-invariant |
| + | is to check whether there is 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. Consider the following systems: | ||
SYSTEMS: | SYSTEMS: | ||
Revision as of 07:56, 11 September 2008
TIME INVARIANCE
A system is defined as "time-invariant" when its output is not an explicit function of time. In other words, if one were to shift the input/output put along the time axis, it would not effect the general form of the function. One of the simplest ways to determine whether or not a system is time-invariant is to check whether there is 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. 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.
