Noise spectrum of the thermal noise?

If we have a thermal noise generated by Brownian stochastic force $\xi (t)$, it has zero mean value. And its correlation function at temperature T is : $$\langle\xi(t) \xi(t^{\prime})\rangle=\frac{\gamma_m}{\omega_m}\int\frac{d\omega}{2\pi}e^{-i\omega(t-t^{\prime})}\omega\left[\coth\left(\frac{\hbar \omega}{2K_BT}\right )+1\right]$$ And it said that the thermal noise spectrum is: $$S_T(\omega)=(\gamma_m/\omega_m)\omega \coth(\hbar \omega/ 2k_BT)$$

So how we derive the noise spectrum?