Single channel blind source separation on the instantaneous mixed signal of multiple dynamic sources

Abstract

Abstract Single Channel Blind Source Separation (SCBSS) has had many algorithms for artificial mixed signal, where the number of mixing sources is assumed to be known, and mixed signal used in validation algorithm only contains two signal sources. However, in real-world application, the mixed number of sources is unknown and is usually more than two. This paper presents a new single-channel blind source separation algorithm based on the multi-channel mapping and Independent Component Analysis (ICA), which supposes that mixed signal comes from a dynamic system in which any component depends on the interaction of other components and signals are linear instantaneous mixture. The mathematical model demonstrates the single channel signal of linear instantaneous mixture. In order to map single channel signals into multi-channel signals, Takens theory and C-C method are used to estimate the time delay and the embedding dimension in the time series of the dynamic system. FastICA for multi-channel blind source separation is improved by using FSS-Kernel (Finite Support Samples Kernel), where the nonlinear function of FastICA is replaced by PDF (probability density function) and estimated by FSS-Kernel. The experiments are conducted to evaluate the proposed algorithm of single channel blind source separation, in which the synthetic signals and speech signals are used respectively. The experiment results show that the proposed method is very effective to estimate the number of independent components and is practical to separate two or more mixed signals.