Download Separation of musical notes with highly overlapping partials using phase and temporal constrained complex matric factorization In note separation of polyphonic music, how to separate the overlapping partials is an important and difficult problem. Fifths and octaves, as the most challenging ones, are, however, usually seen in many cases. Non-negative matrix factorization (NMF) employs the constraints of energy and harmonic ratio to tackle this problem. Recently, complex matrix factorization (CMF) is proposed by combining the phase information in source separation problem. However, temporal magnitude modulation is still serious in the situation of fifths and octaves, when CMF is applied. In this work, we investigate the temporal smoothness model based on CMF approach. The temporal ac-tivation coefficient of a preceding note is constrained when the succeeding notes appear. Compare to the unconstraint CMF, the magnitude modulation are greatly reduced in our computer simulation. Performance indices including sourceto-interference ratio (SIR), source-to-artifacts ratio (SAR), sourceto-distortion ratio (SDR), as well as modulation error ratio (MER) are given.
Download Analysis and Trans-synthesis of Acoustic Bowed-String Instrument Recordings: a Case Study using Bach Cello Suites 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
Download Effective Separation of Low-Pitch Notes Using NMF Using Non-Power-of-2 Discrete 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.