Generalizing the Relative Transfer Function to a Matrix for Multiple Sources and Multichannel Microphones

The Relative Transfer Function (ReTF) describing the acoustic channel between two receivers in response to a single source is a useful tool in many acoustic applications like source localization, separation, and remote microphone methods. In this paper, we propose an approach to generalize the ReTFs of multiple simultaneous sound sources. We allocate receivers into two multichannel groups and formulate the Relative Transfer Matrix (ReTM) to describe the spatial acoustic channel between them. We show that the ReTM is signal independent, a spatial property of the acoustic environment, and that it can be blindly estimated from the observed signals with covariance matrices. We provide preliminary validation on simulated and experiment recordings.