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A novel single-channel blind source separation (SCBSS) algorithm is presented. The proposed algorithm yields at least three benefits of the SCBSS solution: 1) resemblance of a stereo signal concept given by one microphone; 2) independent of initialization and a priori knowledge of the sources; and 3) it does not require iterative optimization. The separation process consists of two steps: 1) estimation of source characteristics, where the source signals are modeled by the autoregressive process and 2) construction of masks using only the single-channel mixture. A new pseudo-stereo mixture is formulated by weighting and time-shifting the original single-channel mixture. This creates an artificial mixing system whose parameters will be estimated through our proposed weighted complex 2-D histogram. In this paper, we derive the separability of the proposed mixture model. Conditions required for unique mask construction based on maximum likelihood are also identified. Finally, experimental testing on both synthetic and real-audio sources is conducted to verify that the proposed algorithm yields superior performance and is computationally very fast compared with existing methods.