Effects of frequency separation in periodic active noise control systems

In many practical active noise control (ANC) applications, the primary noise contains multiple closely-spaced harmonics. A narrow-band feedforward ANC system consists of an adaptive filter excited by a composite reference signal, which is the sum of multiple sinusoids corresponding to the harmonic frequencies of the primary noise. This paper analyzes and shows that the convergence of this direct-form controller 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. This paper also performs mathematical analysis of the direct/parallel-form controller, which significantly improves the convergence speed and reduces filter length by increasing the frequency separation in the individual reference signal for each adaptive filter. Computer simulations are conducted to verify the analysis presented in the paper.