Adaptive filter in wavelet domain under alpha-Stable distribution pulse noise

Since the convergence speed of LMP algorithm is relatively slow, it can not be used in some situations where the demand of real-time processing is very strict. In this paper, the wavelet transform is used in an adaptive filtering structure under alpha-Stable distribution pulse noise. The input signal of adaptive filter is processed by wavelet transform. The large spread in eigenvalues and the condition number are reduced through orthogonal wavelet transform, which results in faster convergence speed directly. And the simulation results indicate that the algorithm proposed in this paper can also obtain the winner solution and has much faster convergence speed and better stable-state performance than that of LMP. Meanwhile, it can choose much bigger step-size than that of LMP, which results in fast convergence speed. So it is convenient for real-time signal processing. In addition, this algorithm is simple and feasible.