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FIR filters with powers-of-two coefficients are attractive for cost-effective implementations. The performance of one such structure, the difference routing digital filter , is discussed. Using an SNR criterion, an optimal algorithm to select the value of the filter coefficients is presented. Results indicate that a 2-3 dB improvement in the SNR can be obtained with this new approach. In addition, the study gives some insight into the relationship between the filter sampling rate, the number of coefficients, and the size of the coefficient alphabet. In particular, it is seen that a tradeoff between the filter sampling rate and the size of the coefficient alphabet exists.