Shift-invariant system

A shift invariant system is the discrete equivalent of a time-invariant system, defined such that if is the response of the system to , then is the response of the system to .[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.

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.

Notes
  1. Oppenheim, Schafer, 12
gollark: Mysterious. I wonder who throws out such things.
gollark: For some reason there was just a 1-hour-to-death CB ice in the AP.
gollark: Running an autorefresher on the eggs helps with hatching them, but they get sick and annoying.
gollark: They just sit there, mocking me by randomly getting sick while simultaneously not hatching.
gollark: Zyumorphs are so annoying.

References
  • Oppenheim, Schafer, Digital Signal Processing, Prentice Hall, 1975, ISBN 0-13-214635-5

See also
  • LTI system theory
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