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.
