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Implementation of FIR filters in the residue number system


N.I. Chervyakov, P.A. Lyakhov

Digital filtering is one of the most important parts of modern digital signal processing. One of the most effective ways of filtering is to use finite impulse response filters, since such filters are much easier to designing and study than the recursive filter (infinite impulse response filters). The authors propose a method of constructing finite impulse response filters in the residue number system, which is an alternative to the traditional positional number system. Application of the residue number system will increase the speed of information processing in applications, the main computational load of the which accounts for the calculation of sums and products. There are two main advantages of modular arithmetic: 1. Arithmetic operations of addition, subtraction and multiplication are performed without division, in contrast to the positional representation of numbers. 2. For each of the values of the moduli residue number system, arithmetic operations are performed with a pair of corresponding residues in parallel. This article describes a 31-th order digital filter and shows a method of designing a filter in residue number system using the software environment MATLAB®. The use of neural network technology to realize filters of this type in practice is proposed. It is shown that the most effective means of neural network realization of devices operating in residue number system, is the use of finite ring neural networks.
May 29, 2020

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