Periodic signal extraction with frequency-selective amplitude modulation and global time-warping for music signal decomposition

A key building block in music transcription and indexing operations is the decomposition of music signals into notes. We model a note signal as a periodic signal with (slow) frequency-selective amplitude modulation and global time warping. Time-varying frequency-selective amplitude modulation allows the various harmonics of the periodic signal to decay at different speeds. Time-warping allows for some limited global frequency modulation. The bandlimited variation of the frequency-selective amplitude modulation and of the global time warping gets expressed through a subsampled representation and parametrization of the corresponding signals. Assuming additive white Gaussian noise, a Maximum Likelihood approach is proposed for the estimation of the model parameters and the optimization is performed in an iterative (cyclic) fashion that leads to a sequence of simple least-squares problems.