Research Of Adaptive Filter Base On Impulse Noise

Non-Gaussian signal processing is important significance and the research focus in the current signal processing field. Ordinarily, the Gaussian assumption is considered to be feasible and can be proved by the central limit theorem in some cases. Moreover, Gaussian assumption can simplify signal processing system design greatly which makes it easy to do theoretical analysis. So many traditional signal processing algorithms are based on the Gaussian assumption. In many practical applications, signals are non-Gaussian and satisfy lowerα-stable distribution which can exactly descript this kind of impulse noise in the image processing, multi-user detection and biomedical science. The Gaussian algorithms are not fit for the lowerα-stable distribution. Therefore, it is required to use fractional lower statistics to design signal processing algorithms. The pth order moment forα-stable distribution is finite and it can be used in adaptive filtering. LMP, NLMP, RLMP algorithm is three kinds of classic algorithms using pth order moment forα-stable distribution.This paper introduces the non-Gaussian stable distribution's mathematical theory and the deduced processing with the practical applications. The NLMP algorithms show good convergence ability and tracing ability. The NLMS algorithms can process both Gaussian and non-Gaussian signal.How to make sure that the algorithm can maintain higher convergence rate in big impulse noise is the key problem. The generalized Burg's formula is processed with fractional lower statistics to get an analogue of NLMP algorithm. The computer simulations show very good convergence ability and this algorithm didn't increase too much computing work. The new algorithm can maintain faster convergence speed when intensity of the impulse signal gradually increased, it shows that the new algorithm has stronger stability.