Analysis of the Frequency Interference in the Narrowband Active Noise Control System

The narrowband active noise control (ANC) algorithm works well in the multi-tone noise reduction system. However, the performance of this algorithm degenerates significantly when the noisy frequencies become very close (e. g. frequency gap is 3 Hz where the sampling frequency is 5000 Hz), which can be seen as frequency interference effects. Up to now, however, this effect has not been researched in detail. In this work, the frequency interference effects are analyzed and discussed. The convergence process, the noise reduction value, the stability condition and the optimum step size are obtained by extensive math formulation derivation, provided two frequencies are close and fixed. Theoretical results show that, tones with large frequency difference can be approximated to independent convergence while the system with close frequencies suffers from poor convergence rate. The value of step size plays an important role in convergence, but the interference effects could never be eliminated by adjusting step size. Simulations are conducted to verify the analysis and the results match well with the analysis.