A shift invariant system is the discrete equivalent of a

time-invariant system In control theory, a time-invariant (TIV) system has a time-dependent system function that is not a direct function of time. Such systems are regarded as a class of systems in the field of system analysis. The time-dependent system function is ...

, 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)

.Oppenheim, Schafer, 12 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.

Applications

Because digital systems need not be

causal Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...

, some operations can be implemented in the digital domain that cannot be implemented using discrete analog components.

Digital filters In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, ...

that require finite numbers of future values can be implemented while the analog counterparts cannot.

Notes

References

* Oppenheim, Schafer, ''Digital Signal Processing'',

Prentice Hall Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari B ...

, 1975,

Applications

Notes

References

See also