Convergence analysis of linear and nonlinear filtered-X LMS algorithms for active control of multitonal noise

In the presence of tonal noise generated by periodic noise source like rotating machines, the filtered-X LMS algorithm is used for active control of such noises. However, the algorithm is derived under the assumption of slow adaptation limit and the exact analysis of the algorithm is restricted to the case of one real sinusoid in the literature. In this paper for the general case of arbitrary number of sources, the characteristic polynomial of the equivalent linear system describing the filtered-X LMS algorithm is derived and a method for calculating the stability limit is presented. Also, a new nonlinear algorithm free from the above assumption is proposed. Simulation results show that in the early stage of adaptation the nonlinear algorithm gives faster decay of errors.