Shift invariant system is the discrete equivalent of the time-invariant system

Time-invariant system

A time-invariant system is one whose output does not depend explicitly on time.This property can be satisfied if the transfer function of the system is not a function of time except expressed by the input and output....

; defined such that if y(n) is the response of the system to x(n), then y(n-k) is the response of the system to x(n-k).

Applications

Because digital systems need not be causal, some operations can be implemented in the digital domain that cannot be implemented using discrete analog components. Digital filters that require finite numbers of future values can be implemented while the analog counterparts cannot.