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In this paper, analysis and trans-synthesis of acoustic bowed string instrument recordings with new non-negative matrix factorization (NMF) procedure are presented. This work shows that it may require more than one template to represent a note according to time-varying behavior of timbre, especially played by bowed string instruments. The proposed method improves original NMF without the knowledge of tone models and the number of required templates in advance. Resultant NMF information is then converted into the synthesis parameters of the sinusoidal synthesis. Bach cello suites recorded by Fournier and Starker are used in the experiments. Analysis and trans-synthesis examples of the recordings are also provided. Index Terms—trans-synthesis, non-negative matrix factorization, bowed string instrument

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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.

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