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Fractional sample interpolation with finite impulse response (FIR) filters is commonly used for motion-compensated prediction (MCP). The FIR filtering can be viewed as a signal decomposition using restricted basis functions. The concept of generalized interpolation provides a greater degree of freedom for selecting basis functions. We developed a generalized interpolation framework for MCP using fixed-point infinite impulse response and FIR filters. An efficient multiplication-free design of the algorithm that is suited for hardware implementation is shown. A detailed analysis of average and worst case complexities compared to FIR filter-based interpolation techniques is provided. Average bitrate savings of around 2.0% compared to an 8-tap FIR filter are observed over the high-efficiency video coding dataset at a similar worst case complexity.