This paper presents theoretical and experimental results about constrained non-negative matrix factorization (NMF) to model the excitation of the musical instruments. These excitations represent vibrating objects, while the filter represents the resonance structure of the instrument, which colors the produced sound. We propose to model the excitations as the weighted sum of harmonically constrained basis functions, whose parameters are tied across different pitches of an instrument. An NMF-based framework is used to learn the model parameters. We assume that the excitations of a well-tempered instrument should possess an identifiable characteristic structure whereas the conditions of the music scene might produce variations in the filter. In order to test the reliability of our proposal, we evaluate our method for a music transcription task in two scenarios. On the first one, comparison with state-of-the-art methods has been performed over a dataset of piano recordings obtaining more accurate results than other NMF-based algorithms. On the second one, two woodwind instrument databases have been used to demonstrate the benefits of our model in comparison with previous excitation-filter model approaches.

In this paper, unsupervised learning is used to separate percussive and harmonic sounds from monaural non-vocal polyphonic signals. Our algorithm is based on a modified non-negative matrix factorization (NMF) procedure that no labeled data is required to distinguish between percussive and harmonic bases because information from percussive and harmonic sounds is integrated into the decomposition process. NMF is performed in this process by assuming that harmonic sounds exhibit spectral sparseness (narrowband sounds) and temporal smoothness (steady sounds), whereas percussive sounds exhibit spectral smoothness (broadband sounds) and temporal sparseness (transient sounds). The evaluation is performed using several real-world excerpts from different musical genres. Comparing the developed approach to three current state-of-the art separation systems produces promising results.