The upper bound of step size for FDPANC algorithm with nonlinear secondary path

Frequency-domain periodic active noise control (FDPANC) algorithm is usually adopted for harmonic noise reduction. In some situations, the secondary path may exhibit nonlinear behavior due to overdriving power amplifiers and transducers. The presence of nonlinear phenomena in the secondary path may significantly decrease efficiency and may even lead to a loss of stability in the system. In this paper, Firstly, the mean-square error (MSE) surface is studied and the stationary points of the MSE surface are classified into two types. Then, the necessary condition for convergence of adaptive filter is derived. Monte Carlo simulations display excellent agreement with the theoretical predictions.