Time Invariance

A system is Time Invariant if and only if the response to the shifted input is equal to the shifted output.

                               x(t-t0) -System-> y(t-t0)
                               x(t) -System-> z(t) -Time Shift t0-> z(t-t0) == y(t-t0)

A system is Time Variant if the shifted input is not equal to the shifted output.

                               x(t-t0) -System-> y(t)
                               x(t) -System-> z(t) -Time Shift t0-> z(t-t0)

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To all math majors: "Mathematics is a wonderfully rich subject."

Dr. Paul Garrett