Simulation of active noise control using transform domain adaptive filter algorithms linked with the inhomogeneous Helmholtz equation

Abstract

An iterative approach is presented that couples the inhomogeneous Helmholtz equation with transform domain active noise control algorithms. The Boundary Element Method is utilized to provide solutions of the inhomogeneous Helmholtz equations for three dimensional pressure wave fields. The source terms in the inhomogeneous Helmholtz equations are adapted iteratively by the algorithm to achieve convergence in the noise cancelling process. The approach can be used to study the impact of active noise control systems based on transform domain algorithms on the wavefield for specific application environments. Additionally, this approach allows for numerical frequency-dependent performance evaluation of multichannel active noise control systems even in acoustically challenging environments. Ill-posed control problems can be identified. The required calculation steps for the integration of the method into existing numerical simulation environments are presented step by step. The study is supplemented by numerical experiments and convergence studies that show good agreement with acoustic theory and analytical results reported in literature.