  The frequency dependent time delay correlation function $K(\Omega)$ is
studied analytically for a particle reflected from a finite one-dimensional
disordered system. In the long sample limit $K(\Omega)$ can be used to extract
the resonance width distribution $\rho(\Gamma)$. Both quantities are found to
decay algebraically as $\Gamma^{-\nu}$, and $\Omega^{-\nu}$, $\nu\simeq 1.25$
in a large range of arguments. Numerical calculations for the resonance width
distribution in 1D non-Hermitian tight-binding model agree reasonably with the
analytical formulas.
