Let{X(t), −∞ < t < ∞} be weakly stationary with covariance function R(s) =

Cov(X(t), X(t+s)) and let R

(w) denote the power spectral density of the process.

(i) Show that R

(w) = R

(−w). It can be shown that R(s) = 1 2π

∞

−∞

R

(w)eiws dw

(ii) Use the preceding to show that

∞

−∞

R

(w) dw = 2π E[X2(t)]