Applications of Adaptive Filtering: Recent Advancements in Active Noise Control

Abstract

ACTIVENOISE CONTROL (ANC) is based on the simple principle of destructive interference of propagating acoustic waves, (Elliot, 2001). The basic idea was proposed in 1936 (Lueg, 1936), however, real applications were quite limited till recently. Thanks to advancement in the algorithms for adaptive signal processing and their implementation using digital signal processors (DSPs); many successful applications of ANC have been reported, themost famous being noise reduction headsets (Gan & Kuo, 2002; Kuo et al., 2006). The most popular adaptive algorithm used for ANC applications is the filtered-x least mean square (FxLMS) algorithm (Kuo & Morgan, 1996) which is a modified version of the LMS algorithm (Widrow & Stearns, 1985). The FxLMS algorithm is computationally simple, but its convergence speed is slow. Different ANC algorithms, with improved convergence properties, have been proposed, viz., 1) lattice-ANC systems (Park & Sommerfeldt, 1996); 2) infinite impulse response (IIR) filter-based LMS algorithms called filtered-u recursive LMS (FuRLMS) (Eriksson et al., 1987), and filtered-v algorithms (Crawford & Stewart, 1997); 3) recursive least squares (RLS) based algorithms called filtered-x RLS (FxRLS) (Kuo & Morgan, 1996) and filtered-x fast-transversal-filter (FxFTF) (Bouchard & Quednau, 2000); and 4) frequency-domain-ANC systems (see (Kuo & Tahernezhadi, 1997) and references there in). There are the following problemswith these approaches: 1) IIR-based structures have inherent stability problems; 2) other approaches mentioned above increase the computational burden substantially; and 3) RLS-based ANC systems have numerical instability problems. These reasons make FxLMS still a good choice for ANC applications, and hence, in this chapter we describe various concepts and methods using FxLMS algorithm. The main objective of this chapter is to provide a comprehensive review of adaptive filtering algorithms developed and employed for ANC systems. We also provide some recent results for two challenging problems: ANC of impulsive-like noise sources, and mitigating effect of the uncorrelated disturbances for which a correlated reference signal is not available. We see that simple modifications and extensions of the existing algorithms and methods improve robustness of the ANC systems. The outline of the chapter is as follows. Section 2 details FxLMS algorithm for feedforward and feedback type ANC systems. It also highlights signal processing issues and open problems for further research. Section 3 describes development of various adaptive algorithm for ANC for Impulsive Noise Sources, and Section 4 addresses issue of Mitigating 2