A new efficient method of adaptive filter using the Galois field arithmetic

Abstract

This paper proposes an efficiently implementation of Multi-Delay Filter Block Recursive Least Squares (MDF-BRLS) algorithm. This implementation uses a particular transform that is defined on a finite ring of integers with arithmetic carried out modulo Fermat numbers. In term of performances, this Fermat Number Transforms (FNT) is ideally suited to digital computation, requiring approximately Nlog2N additions, subtractions and bit shifts, but no multiplications unlike the Fourier transform (FFT). FNT implementation results confirm that the MDF-BRLS adaptive filter can implement with smallest computational complexity compared with an implementation using the Fourier transform.