  In this paper, the Gaussian relay channel with linear time-invariant relay
filtering is considered. Based on spectral theory for stationary processes, the
maximum achievable rate for this subclass of linear Gaussian relay operation is
obtained in finite-letter characterization. The maximum rate can be achieved by
dividing the overall frequency band into at most eight subbands and by making
the relay behave as an instantaneous amplify-and-forward relay at each subband.
Numerical results are provided to evaluate the performance of LTI relaying.
