112 Analjrsis of (:ontinuc,us-Tinie LTT-Systtw:, with the Lnplace Transforiii causal svstc'ms the rc.gion of convcrgeiice lits to the right of a vertical linc throiigh t h c iightltrnost siiigiilnrity, arid wilh xatmiml fraction systeiii funrt ion, 1o thr riglit of I h c riglitixiost pole 'I'hr locatioii of ~ e 5lias no infliimccx on the rcgion of coiicergenct' In order that the Laplwt~t rarisfornr of the oii~putsigiial Y ( s ) in Figurti 6.2 (\xists,the rcgion of coiivcrgeme of the inpiit signal X ( s ) and the furict ion I l ( s ) must overlap As t l r e region5 of coiivergerice for riglit-sidctl input signals arid cauhal systems always overlap, if He( s } i s choscn to be large enough niveigence of the systrrn fimctioii is 1101 normally of iiitcwst Thc gc~icefor system fimd ions iii g m c r i d , not just causal cvtergc' later horn t2ie corwolutiou theorem (C'haytei 8.4.2) r n function was found ic~liziiwly easily Ironi thc nc>tworkiii Scctioii 6.2 re i i s e of c-ornplcx impcdtlnccs It is rvcxi cnrier to detrxrrririe the liaiisfer fiinrtion if an LTI-systrni is gil er1 as a tliffmmtinl eqwtioti (with constant coefficieiits) 1Jse of t he difl'crcntiation throrem (4.26) xepl clvery tle~ivaliwof B fuiictioii of time by a prochct of