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In this paper, we propose an efficient iterative algorithm for finding the minimum sampling frequency for a signal that consists of multiple bandpass signals. This finds important application in software radio where it is desirable to down-convert multiple bandpass signals simultaneously. We will derive a new set of conditions for alias-free sampling for signals that contain multi-band signals. The conditions can be easily examined with few computations. The minimum sampling frequency can be found by iteratively increasing the sampling frequency to meet the alias-free conditions. The simulations demonstrate that the proposed method requires a much lower complexity than existing algorithms.