Fast exact 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 LMS adaptive filter is too computationally-complex to implement. In this paper, we develop a fast, exact implementation of this multichannel system whose complexity is approximately O(2L) per filter channel, where L is the FIR filter length. In addition, we provide a computationally-efficient method for effectively removing the delays of the secondary paths within the coefficient updates, thus yielding a fast implementation 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