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

• Published in: The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS '04 Vol. 2; p. II
• Main Authors: Hinamoto, Y., Sakai, H.
• Format: Conference Proceeding
• Language: English
• Published: New York NY IEEE 2004
• Subjects: Active noise reduction; Algorithm design and analysis; Applied sciences; Circuit properties; Convergence; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Exact sciences and technology; Frequency filters; Least squares approximation; Linear systems; Noise generators; Nonlinear filters; Polynomials; Rotating machines; Stability; Linear system; Noise source; Active system; Noise reduction; Linear filter; Non linear filter; Algorithm; Active control; Algorithm analysis; Least mean squares methods
• ISBN: 9780780383463; 078038346X
• DOI: 10.1109/MWSCAS.2004.1354078

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.