(New page: =Time Invariance= A time invariant system is a system that is not affected by time delays or shifts. =Example of System= If <math>x(t) = a</math>, where <math>a</math> is any real integer...) |
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| + | Given that input is <math>t</math>, in units of time, the system is <math>x(t) = t^4</math> which if shifted would change the final output of the system. At a given time <math>t = 3</math> seconds, <math>t^4 = 81</math>. However, if the time is delayed by <math>t_0 = 2</math> so that the system is <math>x(t-2) = (t-2)^4</math>, then <math>(t-4)^4 = 16</math>. | ||
Latest revision as of 10:14, 12 September 2008
Time Invariance
A time invariant system is a system that is not affected by time delays or shifts.
Example of System
If $ x(t) = a $, where $ a $ is any real integer and $ t $ are inputs in time, then giving it any time delay $ t_0 $ will not affect its value because the value stays constant all times.
Example of Time Variant System
Given that input is $ t $, in units of time, the system is $ x(t) = t^4 $ which if shifted would change the final output of the system. At a given time $ t = 3 $ seconds, $ t^4 = 81 $. However, if the time is delayed by $ t_0 = 2 $ so that the system is $ x(t-2) = (t-2)^4 $, then $ (t-4)^4 = 16 $.
