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In this paper, we apply the voltage overscaling (VOS) technique to the residue-number-system (RNS)-based digital signal processing system for achieving high energy efficiency. To mitigate the soft errors caused by VOS, we propose a new method, called joint RNS-RPR (JRR), which is the combination of RNS and the reduced precision redundancy (RPR) technique. The JRR technology inherits the properties of RNS, including shorter critical path, low complexity, and low power. Moreover, JRR can achieve higher power reduction than RNS for VOS applications. Since the soft errors caused by VOS lead to significant performance degradation of RNS, we use the information from RNS and RPR to achieve a high recovering probability of the soft errors with low hardware complexity. From the case study of finite impulse response (FIR) filter design based on the 0.25- μm 2.5-V CMOS technology, we find that JRR can save 62% more energy compared to the traditional FIR with a less than 2-dB signal noise ratio performance loss. We also find that JRR has lower complexity and better performance than the traditional soft error mitigation methods.