Evaluation of the convergence characteristics of the filtered-x LMS algorithm in the frequency domain

• Published in: Journal of the Acoustical Society of Japan (E) Vol. 16; no. 6; pp. 331 - 340
• Main Authors: Chen, Guoyue, Abe, Masato, Sone, Toshio
• Format: Journal Article
• Language: English
• Published: Tokyo Acoustical Society of Japan 1995
• Subjects: Acoustic signal processing; Acoustics; Active noise cancelation; Convergence characteristics; Exact sciences and technology; Frequency domain evaluation; Fundamental areas of phenomenology (including applications); Physics; Secondary path; The filtered-x LMS algorithm; Signal processing; Frequency response; Active system; Numerical algorithmics; Time response
• ISSN: 0388-2861; 2185-3509; 2185-3509
• DOI: 10.1250/ast.16.331

The convergence characteristics of the time-domain filtered-x LMS algorithm are subject to the distribution of eigenvalues of the autocorrelation matrix of the filtered reference signal. However, evaluation in the time domain does not lead to easy understanding of the physical meaning. This paper presents that the behavior of the filtered-x LMS algorithm in the time domain can be evaluated in the frequency domain if the adaptation process of the filter is slow. The evaluation method presented here facilitates a better understanding of the physical meaning, that is, the convergence characteristics of the algorithm can be evaluated at each frequency (FFT) bin separately, and the effect of the step-size parameter μ, the power gain of the secondary path, and the power spectrum of the reference signal can be evaluated individually at every frequency bin. Furthermore, the evaluation method of the behavior of the adaptive filter in the frequency domain requires fewer computations as compared with those in the time domain. Results of computer simulations of the convergence characteristics of the time-domain filtered-x LMS algorithm estimated in the frequency domain agreed well with the theoretical results.