NMF With Time–Frequency Activations to Model Nonstationary Audio Events

Real-world sounds often exhibit time-varying spectral shapes, as observed in the spectrogram of a harpsichord tone or that of a transition between two pronounced vowels. Whereas the standard non-negative matrix factorization (NMF) assumes fixed spectral atoms, an extension is proposed where the temporal activations (coefficients of the decomposition on the spectral atom basis) become frequency dependent and follow a time-varying autoregressive moving average (ARMA) modeling. This extension can thus be interpreted with the help of a source/filter paradigm and is referred to as source/filter factorization. This factorization leads to an efficient single-atom decomposition for a single audio event with strong spectral variation (but with constant pitch). The new algorithm is tested on real audio data and shows promising results.