Blind source separation via symmetric eigenvalue decomposition

We propose a sufficient condition for separation of colored source signals with temporal structure, stating that the separation is possible, if the source signals have different auto-correlation functions. We show that the problem of blind source separation of uncorrelated colored signals can be converted to a symmetric eigenvalue problem of a special covariance matrix Z(b)=Σ_i=1^L b(p_i)R_z(p_i) depending on L-dimensional parameter b, if this matrix has distinct eigenvalues. We prove that the parameters b for which this is possible, form an open subset of R^L, whose complement has a Lebesgue measure zero. A robust orthogonalization of the mixing matrix is used, which is not sensitive to the white noise. We propose a new one-step algorithm, based on non-smooth optimization theory, which disperses the eigenvalues of the matrix Z(b) providing sufficient distance between them