Fast implementations of the filtered-X LMS and LMS algorithms for multichannel active noise control

In some situations where active noise control could be used, the well-known multichannel version of the filtered-X least mean square (LMS) adaptive filter is too computationally complex to implement. We develop a fast, exact implementation of this adaptive filter for which the system's complexity scales according to the number of filter coefficients within the system. In addition, we extend computationally efficient methods for effectively removing the delays of the secondary paths within the coefficient updates to the multichannel case, thus yielding fast implementations of the LMS adaptive algorithm for multichannel active noise control. Examples illustrate both the equivalence of the algorithms to their original counterparts and the computational gains provided by the new algorithms.