Study of convergence behavior of real-time adaptive active noise control systems

In adaptive active noise control systems, there is a theoretical upper-bound for the adaptation step-size beyond which the adaptation process of the control system becomes unstable. In practice, however, this upper bound is smaller than that suggested in theory. This is mainly because that theoretical analyses have been usually conducted for broadband white noise signals but in practice white noise signals are band-limited. This paper investigates the convergence behavior of a fully implemented real time adaptive active noise control system in an acoustic duct when the primary noise source produces different band-limited white noise. This investigation leads to an empirically-derived expression in closed-form for the upper-bound of the adaptation step size.