In this work, we explore an energy-efficient implementation of the polyphase network for a filter bank multicarrier (FBMC) system. The network is approximated using a greedy algorithm based on matching pursuits (MP) that converts the numerical representation directly from floating point to sum of signed powers of two (SOPOT), which is key for a multiplierless implementation. We compare this technique with other state-of-the-art methods for designing multiplierless hardware, and show that our technique achieves superior performance with similar computational complexity.