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Residue-number-arithmetic digital filters offer major cost and speed advantages over binary-arithmetic digital filters but suffer one major drawback. The filter coefficients must remain constant because efficient means of updating by fractional arithmetic in residue number systems involves time consuming overhead. To maintain high speed in the system the choices are to use RNS in the adders and multipliers with scaling done in ROM, to do RNS multiplies and addditions and scale as part of CRT conversion at the output, or to apply a new fractional NTT interpretation of multiplier output and use RNS throughout. These methods are discussed in this paper.