905. Find the correlation function of a stationary random function $X(t)$, given its spectral density $s_{x}(\omega)=s_{0}$ in the interval $-\omega_{0} \leqslant \omega \leqslant \omega_{0} ;$ outside this interval $s_{x}(\omega)=0$.
Solution. We use the formula

$$
k_{x}(\tau)=2 \int_{0}^{\infty} s_{x}(\omega) \cos \omega \tau \mathrm{d} \omega
$$

Considering that $s_{x}(\omega)=s_{0}$ in the interval ( $0 ; \omega_{0}$ ), we get

$$
k_{x}(\tau)=2 s_{0} \int_{0}^{\omega} \cos \omega \tau d \omega=2 s_{0}\left(\sin \omega_{0} \tau\right) / \tau
$$