Nonlinear Signal Processing Based On Median And Myriad Algorithm

Linear signal processing based on Gaussian distribution assumption is prevalent in the field of signal processing. However, practice has shown that nonlinear systems and non-Gaussian processes emerge in a broad range of applications including underwater acoustic signal, speech signal and biomedical signal. The nonlinear characteristic will cause the dramatic decline of linear algorithm's performances. Nonlinear signal processing, which owns great advantages on non-Gaussian processes, has gained widely recognition and attention in signal processing.This is paper is focused on Median filter and Myriad filter, which are based on the maximum likelihood estimation of generalized gaussian distribution and stable distribution, respectively. By comparisons of linear filter, median filter and myriad filter under different noise environments, the advantages of nonlinear signal processing in non-gaussian environment is readily to see. Especially for myriad filter, with the tunable linearity parameter K , it can work effectively under Gaussian, Cauchy and a wide range of stable distributions.To extend the application of myriad filter, this paper introduced complex signal and complex weights into weighted myriad filter basing on phase coupling and real-imaginary coupling. This provides myriad filter the possibility of performing multi-channel signal processing. Through Matlab simulation, it can remove the noise disturbance in the complex domain effectively.Optimization is important for nonlinear filter to achieve the solid characteristics in signal processing. This paper utilized genetic algorithm in the optimization of weights for nonlinear filters. Since genetic algorithm converges to the global optimum, it has gained large popularity in applications. Simulations demonstrate genetic algorithm outperformed traditional algorithms which are based on least mean absolute (LMA) and least mean square (LMS).To further intensify the application of nonlinear filter, weighted myriad filter has been used to remove the noises in colonic pressure signal. Due to the complexity of biochemical environment, colonic pressure signal contains a lot of noises, while some impulsive noises might be clues of certain disease, the traditional linear filter might remove this important information. By using myriad filter with suitable linearity parameter, the noise can be removed with details of signal well preserved.