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Digital filtering is the core of digital signal processing, since it underlies the solution of most practical problems in this area: noise reduction, amplification and suppression of frequencies, interpolation, decimation, equalization and many others.In recent years DSP applications deals with samples of high bit sizes for improved precisions which required large amount of hardware resources for computation. Irrespective of arithmetic models used for data computation the tradeoff is always exists with word length size. To retain the performance metrics in terms of speed it is essential to invent some mathematics based on modular fields for arithmetic computations. In addition to that, this work also proposes a decomposed LUT based residuegeneration for RNS MACcore that constitutes simpler arithmetic operation which explores improved path delay optimization level. It is proved that inRNS as compared all other functions reverse conversion process is directly influence the overall RNS system performance both in terms of power consumption overhead, performance measures and path delay etc. Here reverse conversion can be implemented using decomposed LUTwhich produces high performance FIR design.
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