Blind source separation with asynchronous signals based on joint optimization of sampling rate offsets and demixing filters

In this work, we propose a blind source separation (BSS) technique designed to handle signals affected by sampling rate offsets (SROs), which commonly occur in distributed recording environments. In the presence of SROs, conventional BSS methods do not work without synchronization. Existing approaches treat synchronization and source separation as a two-stage process: first estimating and correcting the SROs, then performing BSS. In contrast, our method formulates a unified objective function for simultaneously estimating both the SROs and the demixing filters. We apply the auxiliary function method to derive update rules for SROs and demixing filters. Our method is based on the idea that effective source separation fundamentally relies on accurate synchronization, allowing the separation criterion to guide the synchronization process. The core idea is that effective source separation fundamentally relies on accurate synchronization, enabling the separation criterion itself to guide the synchronization process. Furthermore, this integrated framework offers the potential to incorporate prior information, regularization techniques, or machine learning techniques. Experimental evaluations with random SROs and different numbers of sources demonstrate that our method performs comparably to an existing two-stage process, highlighting its potential for real-world applications. Work supported by JST SICORP (JPMJSC2306).