Adaptive system identification based on generalized wavelet decomposition

In this paper, a new adaptive structure based on wavelet packets filter bank (WPFB) is proposed. The system identification of a finite impulse response (FIR) is investigated by utilizing the presented adaptive scheme. When the input signal is lowpass limited, the recursive least squares (RLS) estimation of the adaptive filter weights becomes ill-conditioned. In order to attain the stabilized convergence of the adaptive filters, a regularization parameter is introduced for each wavelet packet to minimize the mean squares error (MSE) of the adaptive filter weights. The analytical expression of the optimal regularization parameter and the optimal initial condition of the RLS algorithm is given. The effectiveness of the proposed approach is demonstrated through simulation examples.