15.1.30 Theory of random processes

Problem: The spectral density of the stationary random function \( X(t) \) is given: \[ S_{X}(\omega)=\frac{1}{\alpha \sqrt{\pi}} \cdot e^{-\frac{\omega^{2}}{4 \alpha^{2}}} . \] Find the correlation function of \( X(t) \).