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Efficient variable-coefficient RNS-FIR filters with no restriction on the moduli set

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Abstract

Introduction of residue number systems (RNS) into hardware realization of high dynamic range FIR filters is known to be advantageous. However, deciding on the number and forms of the moduli, and nature of the filter coefficients is a critical issue, wherein all the previous relevant works lean on RNS multiplication schemes that only work with restricted forms of moduli (e.g., only prime numbers) or only constant FIR coefficients; hence considerably tightening the design space. As a remedy, we propose a modulo-(\({2}^{\mathrm{n}}-\delta \)) multiplier/accumulator scheme (The parameter \(n\) represents the bit-width of the corresponding residue channels wherein the other parameter \(\delta \) determines the exact value of the corresponding modulo) with no restriction on the value of \(\delta \) (except that \(\delta <{2}^{\mathrm{n}-1}\), for balancing the widths of residue channel), nor on the constant/variable nature of the coefficients. The key to this liberty of choice is the especial handling of the end-around carries of modular operations that results in performing only regular non-modular operations, except for the last two that yield the final result. Simulation and synthesis of the proposed circuits show speed, cost and power gains.

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Acknowledgements

This research was supported in part by IPM under Grant CS1400-2-03, and in part by Shahid Beheshti University

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Shahid Beheshti University, Tehran, Iran

    Armin Belghadr & Ghassem Jaberipur

  2. School of Computer Sciences, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    Ghassem Jaberipur

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  1. Armin Belghadr
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  2. Ghassem Jaberipur
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Correspondence to Armin Belghadr.

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Belghadr, A., Jaberipur, G. Efficient variable-coefficient RNS-FIR filters with no restriction on the moduli set. SIViP 16, 1443–1454 (2022). https://doi.org/10.1007/s11760-021-02097-9

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  • DOI: https://doi.org/10.1007/s11760-021-02097-9

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