Analysis of the filtered-X LMS algorithm and a related new algorithm for active control of multitonal noise

• Published in: IEEE transactions on audio, speech, and language processing Vol. 14; no. 1; pp. 123 - 130
• Main Authors: Hinamoto, Y., Sakai, H.
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.01.2006; Institute of Electrical and Electronics Engineers
• Subjects: Acoustic noise; Active control; Active noise control; Active noise reduction; Adaptation; Algorithm design and analysis; Algorithms; Applied sciences; convergence analysis; Detection, estimation, filtering, equalization, prediction; Equivalence; Exact sciences and technology; filtered-X LMS (FXLMS) algorithm; Frequency; Information, signal and communications theory; Least squares approximation; Linear systems; Low-frequency noise; Mathematical analysis; multitonal noise; Noise; Noise cancellation; Noise generators; Polynomials; Rotating machines; Signal and communications theory; Signal, noise; Telecommunications and information theory; Filtering; Simulation; convergence analysis; Noise reduction; Signal processing; filtered-X LMS (FXLMS) algorithm; Algorithm analysis; Active noise control; Mean square error; multitonal noise
• ISSN: 1558-7916
• DOI: 10.1109/TSA.2005.854089

In the presence of tonal noise generated by periodic noise source like rotating machines, the filtered-X LMS (FXLMS) 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 FXLMS algorithm is derived and a method for calculating the stability limit is presented. Also, a related new algorithm free from the above assumption, which is nonlinear with respect to the tap weights, is proposed. Simulation results show that in the early stage of adaptation the new algorithm gives faster decay of errors.