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A shift invariant system is the discrete equivalent of a time-invariant system, defined such that if y {\displaystyle y} is the response of the system to x {\displaystyle x} , then y {\displaystyle y} is the response of the system to x {\displaystyle x}. 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.

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