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Spectrum sensing, a technique to recognize unused or idle spectrum, is a key function for cognitive radio (CR) and requires high precision and fast signal processing technique. To satisfy these requirements, two-stage sensing architecture that combines an energy detector and a feature detector was proposed by IEEE 802.22 working group (WG). For an energy detector, various techniques such as receive signal strength indicator (RSSI), multi resolution spectrum sensing (MRSS), fast Fourier transform (FFT) have been suggested and recently discrete wavelet packet transform (DWPT)-based method was proposed. In this paper, we propose a modified DWPT-based energy detector by using half-band elliptic IIR filters and double threshold method. Through simulation and complexity analysis, it is shown that the proposed scheme can reduce computational complexity and false detection probability compared to conventional DWPT-based energy detector for spectrum sensing in CR.