Wiley signals and systems e book TLFe BO 342

13.4 Tlreoreins of tlie :-'l'ransform 327 of the Laplace trarrsforrn (see Cliaptrr ) T h a t is no coincideticcl ab we saw in Section 13.3.2 that the ansforni of a series can be thotiglit of as : ( w i t inuous-timcsignal g pmely of delta impulses It slioulrl be many properties ol: tlie 1,aplac.e transform also apply to tlic x-transform The most impor tarit tlteorrrri:, of the ;-tuansforrr~arc snnimarised in Table 13.1 They cair i)ISo be sliowri without rcferrirrg to the Laplace transform by iiiscrting them irrto (13 1) In contrast to tlic tlieoiems 01 the Laplace transform the intlc pcnc-lei~tvariable i s deliiied orrly for iiitegei valuc~.In thc square brackets [ 1, no rc pclrmit tecl and corrcspondirigly for the shift thcorcm, only in shifts /t E- Z &reallowed As for the similarity tlieorczn (4.241, for samplt~tlsignals t i w orily scaling of the time axis that i:, pe'rinitted i s cx = -1, so that bccomes the time reversal theorcm for the c-traiisforni Reversing tlie index of a series of values t m i be dorre simply by w d i i i g thcin backwards Tirne-dorrraiii z-domain x X ( x ) 1- b Y ( z ) R W > RC>C{.cJ? ROC(y) Shift, Mult iplicatiorr by k: Time :eversal