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it has a same output. therefore it is a time invariant. | it has a same output. therefore it is a time invariant. | ||
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| + | == example of time variant == | ||
| + | |||
| + | <math>y(t)=3x(5t)</math> | ||
| + | |||
| + | <math>y(t)=x(t-t_0)</math> | ||
| + | |||
| + | <math>z(t)=3y(5t)</math> | ||
| + | |||
| + | <math>=3x(5t-t_0)\leftarrow different output</math> | ||
| + | |||
| + | <math>y(t)=3x(5t)</math> | ||
| + | |||
| + | <math>z(t)=y(t-t_0)</math> | ||
| + | |||
| + | <math>=3x(5(t-t_0))\leftarrow different output</math> | ||
| + | |||
| + | it has a different output. therefore it is a time variant. | ||
Latest revision as of 17:40, 11 September 2008
Def of Time invariant system
when parameter is an invariable, parameter does not change a value depends on time changing.
example of time invariant
$ y(t)=3x(t) $
$ y(t)=x(t-t_0) $
$ z(t)=3y(t) $
$ =3x(t-t_0)\leftarrow same output $
$ y(t)=3x(t) $
$ z(t)=y(t-t_0) $
$ =3x(t-t_0)\leftarrow same output $
it has a same output. therefore it is a time invariant.
example of time variant
$ y(t)=3x(5t) $
$ y(t)=x(t-t_0) $
$ z(t)=3y(5t) $
$ =3x(5t-t_0)\leftarrow different output $
$ y(t)=3x(5t) $
$ z(t)=y(t-t_0) $
$ =3x(5(t-t_0))\leftarrow different output $
it has a different output. therefore it is a time variant.
