Wiley signals and systems e book TLFe BO 164

7.5 Exercises 149 tion 7.1 I) with thc Laplace transform completel) in the frequriicydomain (Sectioris 7.1.4 7.2, 7.3.1, 7.3.2) system itrialysis with the Lnplacc traiisforrn in the freyIier~c.y-clorrr;i~iarid calciilatiori of the iriterrd pail in tEir tirrir-tlomain (Sccl ion 7.3 ) The classical solution is cei tairily the most camplic-atecl nic.thoc1 in terriis of cakuIittion cdfoit as it works cxclubively in the time-clorusin It i\ difficult to guess a par6ictrlar soliitioii for higher-order svstenis If the Laplace transforiii is nsed t o articular solulioii, thr classiral solution tiirns into the$ third proccd~~ie ly in tlw f i rquoncy11 :i~inlysis with t he Liiplacrl !ransforrrr coriipl the inost s i i i t n M e procwlurc i t the internal cttue of the systc’m ih known, for cxaunple, an clecshic*alor prcseiitntioii Then tbr iii\ t i l k 01 ! , h ~iiiitial vdLi(’S ierndl part c m be d&wziiined cithci tr The transfcx 1unc.tion G (s) aird i m t i i c ~ ~ s :ire obtained directly tiorrr t h e te-spmxb representation Cnlritlatiort of tlic Intcmal p a r t in the time-domain i s witable if t1w iiitc~iial structure is unknown, and orilj the difI‘tJreiitia1cqiiation arid the jnitial coiiditiorrs have beer1 givrn ‘Tlir II stiry calculation steps are simple t o carry oiit if the miinei ical values of the tliffvrcrrtridrquatiorr coc4kicirts have bcm provided ises