Fourier transform properties Modulation) ()e/2mod+ YU-fo) Now, cos(x)= +e rej2yf I +x()e -2 x(1)cos(2) Hence, x(t)cos(2for)+ X(-f6)+X(+f Example: x(t= sinc(t), F[sinc(t)]= If Y(t)=sinc(t)cos(2Tf t<=>(1(f-fo)+ll(f+fo))/2 /2 Eytan ModianoΠ π Π Π Fourier transform properties (Modulation) 2π x t e j fot ⇔ X( f − fo () ) e jx + e− jx Now, cos(x) = 2 x t e j fot + x t e− j2πfot x t() cos(2πfot) = () 2π () 2 ( Hence,( x t) cos(2πfot) ⇔ X f − fo ) + X( f + fo ) 2 • Example: x(t)= sinc(t), F[sinc(t)] = Π(f) • Y(t) = sinc(t)cos(2πfot) <=> (Π(f-fo)+Π(f+fo))/2 1/2 Eytan Modiano -fo +fo Slide 7