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In this paper, we first briefly recall the principles of the "time-frequency ratio of mixtures" (TIFROM) approach that we recently proposed. We then show that, unlike independent component analysis (ICA) methods, our approach can separate dependent signals, provided there exist some areas in the time-frequency plane where only one source occurs. We achieve this attractive property because, whereas ICA methods aim at creating independent output signals, we use another concept, i.e. we directly estimate the mixing matrix by using the time-frequency information contained in the observations. Detailed results concerning mixtures of voice and music signals are presented and show that this approach yields very good performance for signals, which cannot be separated with traditional ICA methods.