Fast exact adaptive algorithms for feedforward active noise control

The fast exact least-mean-square (LMS) algorithm is a computationally effic ient method for computing the outputs and updates for an adaptive LMS finit e impulse response (FIR) filter. In this paper, we extend this method to se veral useful algorithms for feedforward active noise control: the filtered- X LMS, modified filtered-X LMS, efficient modified filtered-X LMS, periodic filtered-X LMS, and sequential filtered-X LMS algorithms, respectively. Ch oosing a block size of two produces overall behaviour for these fast exact versions that are identical to their non-block counterparts while reducing the numbers of multiplies by up to 25 per cent over those required by the s tandard algorithms. We then describe Motorola DSP96002 DSP-based implementa tions of the standard and fast exact versions of the filtered-X LMS algorit hm. Our results show that the fast exact implementation can allow a 27.4 pe r cent increase in the filter lengths over those of the standard implementa tion on this processor, which is close to the 33.3 per cent increase that w ould be expected if the number of multiplies were a true indication of an a lgorithm's complexity. Copyright (C) 2000 John Wiley & Sons, Ltd.