Wiley signals and systems e book TLFe BO 321

306 12 The Spectrum of Uiscretc Signals that can be rearranged as The resull is shown in Figure 12.8 Figure 12.8: Magnitiide spectrum of a rectangle scries for clifevent IV Up t o IIOW wc have discussed seyitences in gerternl, without consicleririg where they come lrorn or what they represent Kow we will examine wqucnccs x i k ] , that have tome about; from the sampling of continuous-time signals 2(L) The ~ intiividuaI members of a series xjkl are h e sarnpld valurs of t h continuous-time signal B ( k T ) as in (12.1) According to this simple relationship in the timc-domain a corresponding relationship in the frec~iimcy-dornaiiishotiltl exist that mcaris bvtwcen the Fouricr transform of t h r sampled continuous-time signal and the spectrum of the discretetime signal The sigiial T, ( t )tlerived from the c.oiitimious-timr + p a l F ( t ) with ideal s;timpliiig (see Figure 12.9) will first of all be represented by ifii impulse train Ir(kT)S(t k T ) (12.40) W e expiess t h e weighting of the delta impulses by the values ,c[k]of the discrete- time signal (see (12.1)) (12.41)