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: I wasn't aware of Ligase, but it appears to be missing about a thousand commits from Dendrite, so it is not very useful.
gollark: The root of all this is that Matrix, at least if operating it federated, is mostly based around a really complex room state synchronization protocol, while IRC is just "a message happened" (and channel modes and whatever).
gollark: https://github.com/matrix-org/dendrite#progress
gollark: Looking at those commits, it's missing all the stuff being added to Dendrite to bring it closer to Synapse.
gollark: Versus one 11 hours ago for Dendrite.

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

See also
  • LTI system theory
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.