Convergence analysis of narrowband active noise control

A narrowband feedforward active noise control (ANC) system consists of an adaptive filter excited by the sum of multiple sinusoids corresponding to the harmonic frequencies of the primary noise. The convergence of this direct-form ANC system is dependent on the frequency separation between two adjacent sinusoids in the reference signal. The analysis also proves that the length of the adaptive filter required for achieving the same convergence speed decreases with an increase in frequency separation. Computer simulations are conducted to verify the analysis presented in the paper.