Blind Source Separation Algorithm Based on Kurtosis with Visualization Components

This article presents a comprehensive examination of blind source separation algorithms utilizing kurtosis as the primary statistical measure, with detailed implementation guidelines for visualization subroutines. We begin by introducing the fundamental concept of blind source separation (BSS) and its diverse applications in signal processing domains such as audio separation, biomedical signal analysis, and communication systems. The core algorithm leverages kurtosis - a fourth-order statistical moment that measures the "tailedness" of probability distributions - as an optimization criterion for source separation. Key implementation aspects include whitening preprocessing using eigenvalue decomposition, orthogonal rotation optimization through Jacobi methods, and kurtosis maximization via gradient ascent algorithms.

We subsequently explore the algorithm's advantages in handling non-Gaussian source signals and its computational efficiency compared to higher-order statistics approaches, while addressing limitations in Gaussian signal scenarios and local convergence issues. Practical MATLAB/Python implementation examples demonstrate the algorithm's application to synthetic and real-world mixed signals, featuring code segments for covariance matrix computation and joint diagonalization techniques.

The visualization subsystem architecture receives detailed treatment, covering multi-channel signal plotting routines, convergence curve visualization, and separated component comparison plots. Implementation specifics include dynamic time-domain waveform rendering using matplotlib's subplot functionality, spectral density displays via FFT computations, and interactive 3D scatter plots for source distribution analysis. These visualization tools employ adaptive scaling algorithms and real-time data buffering to handle large-scale signal processing applications effectively.