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Fast and reliable detection of available channels (i.e., those temporarily unoccupied by primary users) is a fundamental problem in the context of emerging cognitive radio networks, without an adequate solution. The (mean) time to detect idle channels is governed by the front-end bandwidth to be searched for a given resolution bandwidth. Homodyne receiver architectures with a wideband radio-frequency front-end followed by suitable channelization and digital signal processing algorithms, are consistent with speedier detection, but also imply the need for very high speed analog-to-digital converters (ADCs) that are impractical and/or costly. On the other hand, traditional heterodyne receiver architectures consist of analog band-select filtering followed by down-conversion that require much lower rate ADCs, but at the expense of significant scanning operation steps that constitute a roadblock to lowering the scan duration. In summary, neither architecture provides a satisfactory solution to the goal of (near) real-time wideband spectrum sensing. In this work, we propose a new compressive spectrum sensing architecture based on the principle of under-sampling (or bandpass sampling) that provides a middle ground between the above choices, i.e., our approach requires modest ADC sampling rates and yet achieves fast spectrum scanning. Compared to other compressive spectrum sensing architectures, the proposed method does not require a high-speed Nyquist rate analog component. A performance model for the scanning duration is developed based on the mean time to detect all idle channels. Numerical results show that this scheme provides significantly faster idle channel detection than the conventional serial search scheme with a heterodyne architecture.