Blind Signal Processing (BSP) of Two-Input Two-Output Linear System for separating Audio Signals using Independent Component Analysis applied in Natural Gradient Algorithm

Abstract

In Blind Source Separation (BSS) the challenge is to recover the source signals from the observed mixed signals. Blindness means that neither the sources nor the mixing system are known. Separation can be based on the theoretically limiting but practically feasible assumption that the sources are statistically independent. The statistical independence of source signals assumption connects BSS and Independent Component Analysis (ICA). The main aim of this research is to solve the separation problem for source signals and mixing system that are not known by comparing two activation functions. The research uses the Natural Gradient Algorithm (NGA) to separate pairs of sub-Gaussian (music), super-Gaussian (speech) and sub-super-Gaussian mixed signals into their original components using Independent Component Analysis (ICA) assumption of statistical independence of the source signals. Two activation functions are used within the NGA for each of the pairs before separation comparison is made. The NGA is formulated using instantaneous Blind Signal Processing where time delay is not factored in the computation of the independent signals. The design uses a 2 x 2 Multiple Input Multiple Output (MIMO) system to accept the pairs of blind audio signals, mix them and separate them to retain their original form or their filtered version. The Fibonacci activation function and the Sigmoid activation functions are used in iterating the coefficients of the NGA up to a hundrend iterations where convergence is realized. Comparing the output (estimated) to the input signals is by waveforms, frequency spectra, and the measure of the Magnitude-Squared Coherence. The results show that the NGA algorithm with Fibonacci and Sigmoid activation function for speech signals pairs yield high performance when compared to other pairs.