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A novel approach to solve the single-channel source separation (SCSS) problem is presented. Most existing supervised SCSS methods resort exclusively to the independence waveform criteria as exemplified by training the prior information before the separation process. This poses a significant limiting factor to the applicability of these methods to real problem. Our proposed method does not require training knowledge for separating the mixture and it is based on decomposing the mixture into a series of oscillatory components termed as the intrinsic mode functions (IMFs). We show, in this paper, that the IMFs have several desirable properties unique to SCSS problem and how these properties can be advantaged to relax the constraints posed by the problem. In addition, we have derived a novel sparse non-negative matrix factorization to estimate the spectral bases and temporal codes of the sources. The proposed algorithm is a more complete and efficient approach to matrix factorization where a generalized criterion for variable sparseness is imposed onto the solution. Experimental testing has been conducted to show that the proposed method gives superior performance over other existing approaches.