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A cognitive radio (CR) system is proposed to operate in the GSM band and the discrete wavelet multitone is adopted as the modulation scheme. This modulation has stronger side-lobe attenuation than the popular OFDM modulation and thus generates much lower adjacent channel leakage, making it suitable for applications with dynamically allocated spectrum. Signal and interference analysis of the adopted DWMT modulation is presented and signal processing techniques that tackle synchronization, equalization, and detection are developed. A DWMT baseband receiver is designed and verified by functional simulation. A digital baseband receiver IC is implemented for the proposed DWMT-based CR system. When the whole GSM band is available, the receiver IC can provide up to 153.6 Mbps of data transmission.