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Use of table look-up multiplication by fractional coefficients allows implementation of high-speed, low-cost recursive digital filters using residue number arithmetic. An 8-bit equivalent filter based on the lossless discrete integrator (LDI) technique described by Bruton can be easily implemented using inexpensive commercially available PROM's for the table look-up. Computer Simulations of first- and second-order LDI-RNS filters indicate substantial cost savings and speed advantages. Experiments on a first-order section verify the basic operation, speed calculations, and cost analysis. Furthermore, extensions to more bits and higher order filters are possible.