(New page: ==Time Invariance== '''If the cascade ''' <math> x(t) \to timedelay \to sys \to z(t)</math> '''yields the same output as the cascade''' <math>x(t) \to sys \to timedelay \to z(t)</math>...) |
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Latest revision as of 13:04, 11 September 2008
Time Invariance
If the cascade
$ x(t) \to timedelay \to sys \to z(t) $
yields the same output as the cascade
$ x(t) \to sys \to timedelay \to z(t) $
for any $ t_{0} $, then the system is called "time invariant".
Example of Time Invariant system
$ X(t)\to sys \to Y(t)=15*X(t) $
$ X(t) \to timedelay \to Y(t)=X(t-t_{0}) \to sys \to Z(t)=15*Y(t)=15*X(t-t_{0}) $
$ X(t) \to sys \to Y(t)=15*X(t) \to timedelay \to Z(t)=15*Y(t-t_{0})=15*X(t-t_{0}) $
Since both the outputs are same we can say that the given system is time invariant.
Example of a Non-Time Invariant system
$ X(t)\to sys \to Y(t)=15*X(2t) $
$ X(t) \to timedelay \to Y(t)=X(t-t_{0}) \to sys \to Z(t)=15*Y(2t)=15*X(2t-t_{0}) $
$ X(t) \to sys \to Y(t)=15*X(2t) \to timedelay \to Z(t)=15*Y(t-t_{0})=15*X(2(t-t_{0}))=15*X(2t-2t_{0}) $
Since both the outputs are different or are not equal we can say that the given system is not time invariant.
