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As the wireless communication services grow quickly, the seriousness of spectrum scarcity has been on the rise gradually. In this context, an emerging technology, cognitive radio (CR) has been come out to solve today's spectrum scarcity problem. Among its fundamental functions, the most important function is spectrum sensing which requires precise accuracy and low complexity. Thus, in this paper, we propose the fast spectrum sensing algorithm using the discrete wavelet packet transform (DWPT) and infinite impulse response (IIR) polyphase filtering schemes. By simulations and complexity analysis, we verify our algorithm.