Shift-invariant system

A shift invariant system is the discrete equivalent of a time-invariant system, defined such that if ${\displaystyle y(n)}$ is the response of the system to ${\displaystyle x(n)}$, then ${\displaystyle y(n-k)}$ is the response of the system to ${\displaystyle x(n-k)}$.^[1] That is, in a shift-invariant system, the contemporaneous response of the output variable to a given value of the input variable does not depend on when the input occurs; time shifts are irrelevant in this regard.