DTFTS of Sums of Complex exponentials Recall ct result: r(t)=c1u←→X()=26(u-) What about dt won X(e1)=? a) We expect an impulse(of area 2T ato=o b) But X(el@) must be periodic with period 2T X(0)=2x∑6(a-o-27 m Note: The integration in the synthesis equation is over 2T period only need X(el) in one 2T period. Thus / 2丌 2丌 ∑6(a-40-27m)lnod m=-0 X(eju)DTFTs of Sums of Complex Exponentials Recall CT result: What about DT: Note: The integration in the synthesis equation is over 2π period, only need X(ejω) in one 2π period. Thus, a) We expect an impulse (of area 2π) at ω = ωo b) But X(ejω) must be periodic with period 2π In fact