Abstract: We determine the informaion capacity of the linear, time-varying communications channel with additive white Gaussian noise for transmission signals with support approximately restricted to closed regions of the time and frequency domains. We address the two-part problem of first, constructing appropriate transmission functions, and second, determining the mutual information. Our approach provides a signaling set that is adaptive to the time and frequency stability of the channel, and we use this set to estimate the channel's information capacity. In the limiting regime, this approach recovers the time-invariant capacity up to a redundancy factor.