Time Invariant System
"A system is called "time invariant" if for any input signal x[n] and for any $ t_0 \epsilon \mathbb{R} $, the response to the shifted input is the shifted output." -Mimi Boutin
Time Variant System
A system is considered "time variant" if time shifting the input x[n] does not produce the same result as the output shifted by the same amount.
