Shift invariant system is the discrete equivalent of the time-invariant system; 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).
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.
- Oppenheim, Schafer, 12
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