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Relative to the Triple Modular Redundancy (TMR) scheme, the arithmetic residue codes based fault-tolerant DSP design consumes much less resources. However, the price for the low resource consumption is the fault missing problem. The basic tradeoff is that, smaller modulus used for the fault checking consumes fewer resources, but the fault missing rate is higher. The relationship between the value of modulus and the fault missing rate is analyzed theoretically in this paper for fault-tolerant FIR filter design, and the results are verified by FPGA implemented fault injections.