Development and analysis of optimized narrowband ANC systems
In this thesis, the research on narrowband active noise control (ANC) systems is presented. The effect of the secondary path transfer function on the convergence of the filtered-x least mean-square (FXLMS) algorithm is studied. An optimized FXLMS algorithm for narrowband ANC is developed and analyzed by using eigenvalue and eigenvector techniques. The FXLMS algorithm convergences very slowly at the frequency components corresponding to valleys of the magnitude response of the secondary path S'(.z), when the magnitude response of the secondary path is not flat. To compensate for this effect, we propose an optimized FXLMS algorithm in which the reference signal is a combination of sinusoids with optimized amplitudes instead of unit amplitudes. Amplitudes of sinusoids are chosen according to the magnitude response of the S(z) and the exact expression of the optimum amplitudes is derived. Also, the eigenvalues of the covariance matrix of both the optimized and the traditional FXLMS algorithms are estimated and compared. It is shown that the optimized algorithm converges faster. Computer simulation results are conducted to compare the optimized FXLMS algorithm with the traditional one. The optimizing method is also extended to the multiple filters connecting with direct/parallel form. In this case, the ANC system includes multiple sinewave generators and corresponding adaptive filters. Each sinewave generator produces a reference signal which- contains one or more sinusoids. The amplitudes of sinusoids in each reference signal are optimized according to the magnitude response of the S(z). Both the eigenvalue analysis and computer simulations show that the optimized algorithm also converges faster in this case.