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B.) h2(t) = 6t*x2(3t) + 5 | B.) h2(t) = 6t*x2(3t) + 5 | ||
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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. | ||
Revision as of 07:57, 11 September 2008
TIME INVARIANCE
Definition 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.
Method
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.
