## Statistical Pattern Recognition: Fourier

Prove that $E[\bold{F}(j \omega_{1})\bold{F}^{*}(j \omega_{2})) = 0$ for $\omega_1 \neq \omega_2$ where $\bold{F}(j \omega)$ is the Fourier transform of a stationary random process, $\bold{x}(t)$ as $F(j \omega) = \int_{-\infty}^{\infty} x(t)e^{-j \omega t} \ dt$.

So if $\omega_1 = \omega_2$ then the expected value is zero.