Effective separation of low-pitch notes using nmf with non-power-of-2 short-time Fourier transforms

Recently, non-negative matrix factorization (NMF), which is applied to decompose signals in frequency domain by means of short-time Fourier transform (STFT), is widely used in audio source separation. Separation of low-pitch notes in recordings is of significant interest. According to time-frequency uncertainty principle, it may suffer from the tradeoff between time and frequency localizations for low-pitch sounds. Furthermore, because the window function applied to the signal causes frequency spreading, separation of low-pitch notes becomes more difficult. Instead of using power-of-2 FFT, we experiment on STFT sizes corresponding to the pitches of the notes in the signals. Computer simulations using synthetic signals show that the Source to Interferences Ratio (SIR) is significantly improved without sacrificing Sources to Artifacts Ratio (SAR) and Source to Distortion Ratio (SDR). In average, at least 2 to 6 dB improvement in SIR is achieved when compared to power-of-2 FFT of similar sizes.