Blind separation using adaptive nonlinear functions controlled by kurtosis

摘要

Convergence and separation performances are highly dependent on a relation between probability density functions (pdf) of signal sources and nonlinear functions used in updating coefficients of a separation block. This relation was analyzed based on kurtosis κ{sub}4. It was suggested that tanhy and y{sup}3, where y is the output, ale useful nonlinear functions for super-Gaussian (κ{sub}4 > 0) and sub-Gaussian (κ{sub}4 <0), respectively. In this paper, an adaptive nonlinear function is proposed. It has a form of f(y) = a tanhy + (1 - a)y{sup}3/4, where a is controlled by kurtosis. It is assumed that the pdf p(y) of the output signal y satisfies the stability condition f(y) = (dp(y)/d(y)/p(y). Based on this assumption, the parameter a and the kurtosis is related. First, the kurtosis is calculated for given a, which takes value in 0 ≤a ≤ 1. Next this numerical relation is approximated by a function a = q(κ{sub}4). In a learning process, κ{sub}4(n) of the output signals is calculated at each sample n, and a is determined by a(n) = q(κ{sub}4(n)). Then, the nonlinear function f(y) is adjusted. Blind separation of music signals of 2～5 channels were simulated. The proposed method is superior to a method, which switches tanhy and y{sup}3 based on polarity of κ{sub}4(n).