In this paper, we propose a novel digital filter-and-forward full-duplex (FF-FD) relaying system to exploit the loop-back signal (LBS). Unlike treating the LBS as a generic interference, we utilize the fact that the LBS actually conveys redundant information from the source to the destination in the relaying communication scenarios. Thus, the LBS could potentially be exploited instead of being cancelled. We prove that the FF-FD can achieve higher system achievable rate (SAR) than the amplify-and-forward full-duplex (AF-FD) system. To maintain the system linearity, a digital FF-FD relay is proposed without non-linear distortion induced in the digital domain. The relay can be modeled as a linear digital filter to exploit the LBS via linear filtering. The design challenge at the relay is accordingly shifted to optimizing its discrete frequency response (DFR) rather than the complicated interference cancellation design. Based on the metric of maximum SAR, the DFR is efficiently optimized with and without CSI at the source. A low-complexity yet near-optimal alternative is also provided to reduce the computation cost for large multi-carrier systems. Both theoretical analyses and simulations validate the considerable advantages of the proposed FF-FD over the conventional AF-FD, making FF-FD an appealing candidate for future relaying communications.