Separation of musical notes with highly overlapping partials using phase and temporal constrained complex matrix 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.