An algorithm for exploiting sparsity of the underlying source signals in either the time or time-frequency domain is introduced. Utilizing the sliding ratio signal (SRS) derived from at least two observed mixture signals, the often separate processing of estimating the number of sources and the mixing matrix (or overcomplete dictionary) are simultaneously detected for reduced computational load. For instantaneous mixtures, the observed signals are directly processed by the SRS algorithm which detects the major modes of ratio signals when the relative time delays of a source are equalized in both mixtures. For convolutive mixtures, the sliding discrete Fourier transform (SDFT) window is used to facilitate instantaneous de-mixing in the time frequency domain. The sliding Goertzel algorithm is used for pre-processing the the convolutive mixtures to reduce the room impulse response inter-symbol interference effects. The time-frequency signals, at a frequency bin of choice, are then used by the SRS algorithm to learn the mixing process such that sparse decay algorithms can separate the underlying source signals. The SDFT approach and sliding Goertzel algorithm greatly decrease the computational load compared to most time-frequency based methods which tend to suffer from permutation and scaling ambiguities of the estimated sources. Simulation results are provided to illustrate the performance of the proposed algorithm.
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