A New Robust Narrowband Active Noise Control System in the Presence of Frequency Mismatch

Narrowband active noise control (ANC) systems have many real-life applications where the noise signals generated by rotating machines are modeled as sinusoidal signals in additive noise. However, when the timing signal sensor, such as a tachometer used to identify the signal frequencies, and the cosine wave generator contain errors, the frequencies of reference sinusoids fed to each ANC channel will then be different from the real primary noise signal frequencies. This difference is referred to as frequency mismatch (FM). In this paper, through extensive simulations, we first demonstrate that the performance capabilities of a conventional parallel form narrowband ANC system using the filtered-x LMS (FxLMS) algorithm degrades significantly even for an FM as small as 1 %. Convergence of the algorithm in the mean sense is also analytically investigated for a better understanding of its performance degradation. Next, we propose a new narrowband ANC system that successfully compensates for the performance degradations due to the FM. The amplitude/phase adjustment of reference sinusoids and the FM mitigations in the proposed system are performed simultaneously in a harmonic fashion such that the influence of the FM can be removed almost completely. Simulations as well as application to a real noise signal are provided to demonstrate the effectiveness of the proposed new system