Time Invariance

Time invariance implies that the specific time at which the input is applied does not matter. A delay in the input simply reflects a delay in the output.

As an example of time variance, consider that the best time for our peak physical performance is late afternoon or early evening. A cyclist doesn’t cover the same distance at all times of the day. At midnight or noon, their performance suffers.

Definition

A system is time invariant if a delayed input results in a delayed output and remains unchanged otherwise. Mathematically, for an input $x[n]$ and output $y[n]$:

$$x[n] \qquad \rightarrow \qquad y[n]$$

We should have the following for a delay of ...