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We consider discrete-time channels with finite-length intersymbol interference and additive Gaussian noise. The channel noise is considered to be a stationary ARMA (autoregressive and/or moving average) Gaussian process. We assume that the channel is used with feedback and compute the maximal feedback information rate achievable by stationary power-constrained sources. We show that feedback-dependent Gauss-Markov sources achieve the feedback capacity, and a Kalman-Bucy filter is optimal for processing the feedback. We then formulate the capacity computation into a system of equations whose solution gives the optimal signaling and the feedback capacity for stationary sources. In general, the equations are solved numerically, but for first-order channels, the problem admits a closed form solution.