Dynamic properties of feedback active noise control with sinusoidal primary noise

Feedforward active noise control (ANC) system requires a coherent reference signal. However, in many real-life applications, this reference signal may be unavailable. Feedback ANC systems are promising for such cases. So far, to the best of our knowledge, stochastic analysis of feedback ANC systems has not appeared, and our work is expected to fill in this gap. In this paper, dynamics of a feedback ANC system is analyzed in the context of sinusoidal noise control based on relationship of discrete Fourier coefficients among reference signal, secondary source, residual noise etc.. Difference equations governing the dynamics of the system are derived and discussed in detail. Extensive simulations are conducted to demonstrate the validity of the analytical results.