Fast exact adaptive algorithms for feedforward active noise control

Abstract

The fast exact least-mean-square (LMS) algorithm is a computationally efficient method for computing the outputs and updates for an adaptive LMS finite impulse response (FIR) filter. In this paper, we extend this method to several 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. Choosing 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 standard algorithms. We then describe Motorola DSP96002 DSP- based implementations of the standard and fast exact versions of the filtered-X LMS algorithm. Our results show that the fast exact implementation can allow a 27.4 per cent increase in the filter lengths over those of the standard implementation on this processor, which is close to the 33.3 per cent increase that would be expected if the number of multiplies were a true indication of an algorithm's complexity. Copyright © 2000 John Wiley & Sons, Ltd.