THE STABILITY AND CONVERGENCE CHARACTERISTICS OF THE DELAYED-X LMS ALGORITHM IN ANC SYSTEMS

✍ Scribed by G. Chen; T. Sone; N. Saito; M. Abe; S. Makino

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 256 KB
• Volume: 216
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.1719

✦ Synopsis

The Delayed-x LMS algorithm is a simplified version of the Filtered-x LMS algorithm, in which the model C of the secondary path C from the adaptive filter output to the error sensor is represented by a pure delay of k samples (the delayed model D) in order to reduce system complexity. However, the simplification produces a modelling error, which deteriorates the ANC performance. In this paper, the stability, especially that of the convergence characteristics of the feedforward active noise control system with the Delayed-x LMS algorithm, is investigated. It is shown that the stability condition is one in which the phase error (the phase difference between the secondary path C and its delayed model D) is in the range between -p/2 and p/2. Furthermore, it is shown that if the phase error is large, a small step-size parameter m should be adopted to achieve stable noise cancellation, though the convergence speed becomes slow in the frequency domain. The theoretical results are verified by computer simulations.