Stability analysis of an active noise control system using single adaptive filter with an external injection noise and an acceleration method of adaptive algorithm

In this paper, the stability analysis of an active noise control system using single adaptive filter with an external injection noise and an acceleration method that makes use of the property of this noise are discussed. The convergence performance of this adaptive algorithm is analyzed from the viewpoint of a property of the Hessian matrix. As a result, it is proved that the Hessian matrix is positive definite even when the power density spectrum of the noise source signal and the external injection noise are different. Furthermore, by selecting the power density spectrum of the external injection noise to be the inverse property of that of the noise source, it is proved that the system with the white noise source and the white injection noise can be realized. Finally, these theoretical considerations are verified by computer simulation. © 2019 The Institute of Electrical Engineers of Japan.