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In this correspondence, we propose a new iterative algorithm for finding the minimum sampling frequency of a signal that consists of multiple bandpass signals. This finds important application in software radio where it is desirable to downconvert multiple bandpass signals simultaneously. We will derive a new set of conditions for alias-free sampling. The minimum sampling frequency can be found by iteratively increasing the sampling frequency to meet the alias-free conditions. We will show how the algorithm can be generalized to find alias-free sampling frequency intervals. Simulations will be given to demonstrate the usefulness of the proposed method.