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Bandpass sampling (BPS) techniques for the direct down-conversion of RF bandpass signals have become an essential technique for software defined radio (SDR), due to their advantage of minimizing the radio frequency (RF) front-end hardware dependency. This paper proposes an algorithm for finding the minimum BPS frequency for simultaneously down-converting multiple RF signals through full permutation over all the valid sampling ranges found for the multiple RF signals. We also present a scheme for reducing the computational complexity resulting from the large scale of the purmutation calculation involved in searching for the minimum BPS frequency. In addition, we investigate the BPS frequency allowing for the guard-band between adajacent down-converted signals, which help lessen the severe requirements in practical implementations. The performance of the proposed method is compared with those of other pre-reported methods to prove its effectiveness.