▁the ▁trans ient ▁part ▁of ▁a ▁signal . ▁ ▁The ▁step ▁response ▁can ▁be ▁multip lied ▁with ▁other ▁signals ▁to ▁show ▁how ▁the ▁system ▁respond s ▁when ▁an ▁input ▁is ▁suddenly ▁turned ▁on . ▁ ▁The ▁unit ▁step ▁function ▁is ▁related ▁to ▁the ▁Di rac ▁delta ▁function ▁by ; ▁ ▁Systems ▁ ▁Linear ▁time - in variant ▁( LT I ) ▁Linear ity ▁means ▁that ▁if ▁you ▁have ▁two ▁inputs ▁and ▁two ▁corresponding ▁outputs , ▁if ▁you ▁take ▁a ▁linear ▁combination ▁of ▁those ▁two ▁inputs ▁you ▁will ▁get ▁a ▁linear ▁combination ▁of ▁the ▁outputs . ▁An ▁example ▁of ▁a ▁linear ▁system ▁is ▁a ▁first ▁order ▁low - pass ▁or ▁high - pass ▁filter . ▁Linear ▁systems ▁are ▁made ▁out ▁of ▁analog ▁devices ▁that ▁demonstrate ▁linear ▁properties . ▁ ▁These ▁devices ▁don ' t ▁have ▁to ▁be ▁entirely ▁linear , ▁but ▁must ▁have ▁a ▁region ▁of ▁operation ▁that ▁is ▁linear . ▁ ▁An ▁oper ational ▁ampl ifier ▁is ▁a ▁non - linear ▁device , ▁but ▁has ▁a ▁region ▁of ▁operation ▁that ▁is ▁linear , ▁so ▁it ▁can ▁be ▁mode led ▁as ▁linear ▁within ▁that ▁region ▁of ▁operation . ▁ ▁Time - in var iance ▁means ▁it ▁doesn ' t ▁matter ▁when ▁you ▁start ▁a ▁system , ▁the ▁same ▁output ▁will ▁result . ▁For ▁example , ▁if ▁you ▁have ▁a ▁system ▁and ▁put ▁an ▁input ▁into ▁it ▁today , ▁you ▁would ▁get ▁the ▁same ▁output ▁if ▁you ▁started ▁the ▁system ▁tom orrow ▁instead . ▁ ▁There ▁aren ' t ▁any ▁real ▁systems ▁that ▁are ▁L