Blind Source Separation Using Time-Delayed Dynamic Mode Decomposition

Blind Source Separation (BSS) is a significant field of study in signal processing, with many applications in various fields such as audio processing, speech recognition, biomedical signal analysis, image processing and communication systems. Traditional methods, such as Independent Component Analysis (ICA), often rely on statistical independence assumptions, which may limit their performance in systems with significant temporal dynamics. This paper introduces an extension of the dynamic mode decomposition (DMD) approach by using time-delayed coordinates to implement BSS. Time-delay embedding enhances the capability of the method to handle complex, nonstationary signals by incorporating their temporal dependencies. We validate the approach through numerical experiments and applications, including audio signal separation, image separation and EEG artifact removal. The results demonstrate that modification achieves superior performance compared to conventional techniques, particularly in scenarios where sources exhibit dynamic coupling or non-stationary behavior.