(TIME INVARIANCE)
(TIME INVARIANCE)
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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 in 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:
+
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.


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