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The capacity of a degraded relay channel with inter-symbol interference and additive colored Gaussian noise is examined under an input power constraint. Using the classical methodology, a related channel and signal model is developed - the circular degraded relay channel - the capacity of which is shown to be equivalent to that of the channel of interest in the limit of infinite block length. The capacity of circular relay channel is, in turn, determined by the decomposition into parallel degraded relay channels whose individual capacities are given by prior results. Two case studies based on the degraded relay channel with memory and white noise are examined: Common transmission bandwidths on each link and different effective transmission bandwidth over each link.