With the ever-increasing applications for digital signal processing, there is a strong motivation to discover new processing techniques. Methods based on matrix rank minimization have been increasingly used for signal analysis, particularly for signal separation. This research considers the analysis and application of the Non-Negative Matrix Factorization (NMF), associated with Kullback-Leibler and Itakura-Saito divergences, for the separation of digital sound sources consisting of harmonic and percussive elements. The NMF algorithm and divergence functions were implemented in a MATLAB environment and applied to musical mixes composed of electric guitar, bass, kick, ride, and snare. Then, comparative analyses of the divergence functions performance used SNR-based metrics. Considering the inconsistencies between the objective metrics and the human perception, two alternative objective metrics were proposed for the Signal-Interference Ratio (SIR), called Windowed SIR (W-SIR) and Average Windowed SIR (AW-SIR). Based on the W-SIR metric, the authors present the new Recursive Semi-Supervised NMF (RSS-NMF), for which the training information is extracted from the original signal. In both cases, the results demonstrated better performance of the RSS-NMF technique in relation to the non-supervised NMF technique.
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