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

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 Nlog₂ N 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. (paper)