  We consider linear time-varying channels with additive white Gaussian noise.
For a large class of such channels we derive rigorous estimates of the
eigenvalues of the correlation matrix of the effective channel in terms of the
sampled time-varying transfer function and, thus, provide a theoretical
justification for a relationship that has been frequently observed in the
literature. We then use this eigenvalue estimate to derive an estimate of the
mutual information of the channel. Our approach is constructive and is based on
a careful balance of the trade-off between approximate operator
diagonalization, signal dimension loss, and accuracy of eigenvalue estimates.
