Wiley signals and systems e book TLFe BO 305

290 11 Sampling and Periodic Signals and Xi = sa mplcd'! For which cases does aliasing occur? Exercise 11.16 A sigiiad ~ ( t=) -hi wq 271 What rases arc critically (y ) is sampled at eqniciistant points in time i/T, v E z l o form a signal Z A ( ~ )of weighted delta impulses a) Give the origirial spectrurn X ( j j ) = F{z(L))(sketxh b) Sketch tlie spcx:trimi X n ( j w ) a - o Z A ( ~ )for with Iabelled axes) 2n the case T = - 3w!? Exercise 11.17 The sketched rectangular signal r(t) will be inriestigat ed 4n 1i a a,) Whaf is the spectrum R ( j w ) = F ( r ( t ) }of the sigial for hoth ixra,gnitude and phase? Sketch i R ( j w )1 1)) The spec.trum R(.7w) is saiiiplcd at equidistant points spaced by uo.This cieates the ilew sprctmm: x R(JW1) 6(w - Jm) Ru(3.1.')= WO u=-m Sketch the magnitude of this new spectrum for lwl $ with a) w* = x 47'' 27r 4) WO = fl, Y) WO = F, where the weighted delta iiiipulses arc rcpreseiitrtl by arrows of rorrwpondilig length c) Slcetcli the hictioiis of time r , ( f ) , corrcspondirig to the eases t v ) , f i ) , y ) in part, b)