domain licts the prirntlrv goal of making ( ill(~l1lftti(>ns siiiiplty to cairy o i i ~than I hey ~ v o ~ be l d in the tirne-domain The first c*xarriple of this i s the evaluation t m response, which rim he wprcsentccl in tire fiequeric y-dor~i;tittit(i a miiiiltiplication by the bystcwi fii n, but 111 tlre tiinr.-cloinain rcqiiirps 1he uscl ol the corivohition integral As a, ntl ex;tinplc VEV giw the arrdysis in natural resonancci whicli is (io siinplc ie frequericy-tlomniu using partial fractions hi)wcm~r,vile‘ have (,hat we limv nwer doire it iii the tirrie-domain In ,211 returrretl to the time-domain after rrsirrg the advintages LVcA l w , ~rarcl) at tempted t o clrai a c t w i s c or dehign roperties in L ~ frecluency-cloMiaiii P The oirlj t i m e bring the description of 111fiiiictiori by the poles and zeros in the cornplcx s-plane (sw C'hapter 6.3) J lie iriterprct at i o n of w c l i polc-zero plots is riot so siriiple, h o ~ c ~ / ebtcarise r, the systeiri function i\ a c.ornp1~xfnnction oi to1 variablPs It fails completclv eiitiai e q u a \ b n with cmist;trit cocflicie~h,fbr example, rf ilc1,iy circuit H ( s ) has t o be niialytic in the region of ronvcigcrice, dc s-planr is diffictilt as this property mav be violated The following point siiriiniar tage5 of the Laplace tiaiisform r l Ii; oiilv pmvides a simple bc> dcscrihed by o r t i i n q ~diI 111 iriotlel for UI'I-systcxrrc; that c m ations with ( onstnrit c-oeilicicwts The l,,tplace transloorm tlc fuiirtioris of Ilrl-svsteins, xist tor sigiials cst, that axe eigerr- E - ~thr systein fuiictiorr, (he piopclit ies of a rrr 1x1 thr Srcquencv domain As an alteriiative to the Laplace transform, wc' iiow cwiisrd(>rt2iv Fouricy transthat it owrcornes thc stated disadvm?tagesof t he L ~ p l a c rtransf'orrn while also Iwepirrg m m y of the riicrits ie