The objective of this study was to develop a technique for differentiation of two instantaneous audio signals recorded concurrently by two microphones. To achieve this objective, a signal was first subjected to Short Time Fourier Transform (STFT), then each frequency bin was processed individually by a two-phase technique consisting of an estimation of orthogonalization matrix and rotation matrix in that order. The proposed method introduces a new geometric approach to the separation of sparse signals. In fact, it introduces two new steps for the general BSS technique. In fact, these two steps are presented in this paper instead of the whitening and rotating steps in blind speech separation algorithms. This paper separates audio sources in difficult situations with significant improvements in algorithm performance. Therefore, the experiments were performed in difficult conditions, such as when the microphones are collinear, short distances of microphones and having short sources. Therefore, the experiments were performed in difficult conditions. Performance of the proposed method was evaluated by a number of numerical examples. The experiments were performed using the Roosim simulator, and the results showed that the proposed algorithm is a simple and useful solution for separating two speech signals recorded with two microphones.
