Techniques for residue-to-analog conversion for residue-encoded digital filters

Recent papers have reported that the use of residue number coding in digital filters can result in better speed/cost ratios when compared to filters designed with conventional adders and multipliers. This paper presents two approaches to the design of residue-to-analog converters to be used with residue number filters. The first approach, based on the associated mixed radix number system, is particularly useful when it is desired to translate the residue samples directly into analog form. The second approach, based on the Chinese remainder theorem, is a more direct method for translating from residue to weighted binary representation. A hardware feasibility model is described that was constructed to demonstrate the conversion principles.