shiftinvariance
Shift invariance is a property of a function, operator, or system with respect to translations in its input. A system is shift-invariant if translating the input by a fixed amount results in a corresponding translation of the output by the same amount. Formally, let S_a denote the shift operator that maps an input x(t) to x(t − a). A system F is shift-invariant if for all inputs x and all a, F(S_a x) = S_a(F x). This means the system’s behavior does not depend on the absolute position of the input.
In signal processing, shift invariance is closely related to the concept of time invariance. A time-invariant
Shift invariance is not universal; some systems are shift-variant, meaning their response depends on the input’s