Nonlinear adaptive noise suppression based on wavelet transform

The conventional linear adaptive filters are not effective for discriminating the transient wideband signal components from noise. A recently developed wavelet shrinkage approach is able to maintain the function local regularity while suppressing noise however, it has only been used in function estimation problems. In this paper, a new type of nonlinear filtering method for adaptive noise suppression is presented, based on shrinkage method. A new class of shrinkage functions is also presented. The filtering structure and the learning algorithm are developed. The theoretical analysis proves convergence in certain statistical sense. The numerical results of our system are presented for both the standard and the new shrinkage function and compared with the conventional linear adaptive filter based techniques. Results indicate that both the optimal solution and the learning performance are superior to the conventional methods. It is shown that our new shrinkage function performs better than the standard shrinkage function.