Time Invariance

A system is called time invariance if and only if:

$x(t) --> [system] --> [time delay] --> y(t)\,$

yields the same result as

$x(t) --> [time delay] --> [system] --> y(t) \,$

Remember: delay --> for only every function of t, change the t into t with the offset

Example of a time invariance system

$y(t) = x(t) \,$

$x(t) --> [system] --> x(t) --> [timedelay] --> x(t-1) \,$

it yields the same result as:

$x(t) --> [timedelay] --> x(t-1) --> [system] --> x(t-1) \,$

$y(t) = t * x(t) \,$

$x(t) --> [system] --> t * x(t) --> [timedelay] --> t * x(t-1) \,$

it yields not the same result as:

$x(t) --> [timedelay] --> x(t-1) --> [system] --> (t-1) x(t-1) \,$