Power Spectrum of a random process If x(t is wSS then the power spectral density function is given by Sx ( = F[R] The total power in the process is also given by: S, (df=R,(e 72nd df Rr (tJe / df dt R(Je tiu df at=R,(8(tWt=R(O)τ Power Spectrum of a random process • If x(t) is WSS then the power spectral density function is given by: Sx(f) = F[Rx(τ)] • The total power in the process is also given by: ∞ ∞  ∞  Px = ∫ Sx () t e− j ftdt f df = df ∫  ∫ Rx ( ) 2π −∞ −∞−∞  ∞  ∞  x () 2π = ∫  ∫ R t e− j ftdf  dt −∞−∞  ∞  ∞  ∞ = ∫ R t 2π t t dt = Rx (0) x ( ) ∫ e− j ftdf  dt = ∫ Rx ( )δ() −∞ −∞  −∞ Eytan Modiano Slide 4